Question 1

Determine whether the statement is true or false. ​
If f(x)= x + 1 and g(x)= 5x,then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .
​

Accepted Answer

A) False 
B) True 
A) False 
B) True A

Question 2

Let f (x)= 2x + 1,g(x)= 3x - 2.Find the function.​ $( f - g ) ( x )$ ​

Accepted Answer

A)  $( f - g ) ( x ) = \frac { 2 x + 1 } { 3 x - 2 }$ 
B)  $( f - g ) ( x ) = 3 - x$ 
C)  $( f - g ) ( x ) = 6 x ^ { 2 } - x - 2$ 
D)  $( f - g ) ( x ) = 5 x - 1$ 
E) none of the above 
A)  $( f - g ) ( x ) = \frac { 2 x + 1 } { 3 x - 2 }$ 
B)  $( f - g ) ( x ) = 3 - x$ 
C)  $( f - g ) ( x ) = 6 x ^ { 2 } - x - 2$ 
D)  $( f - g ) ( x ) = 5 x - 1$ 
E) none of the above B

Question 3

The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by $r ( t ) = 2.25 \sqrt { t }$ ,where r is the radius in meters and t is the time in hours since contamination. ​
Find a function that gives the area A of the circular lake in terms of the time since the spread began.
​

Accepted Answer

A)  $A \circ r ( t ) = 5.0625 \pi \sqrt { t }$ 
B)  $A \circ r ( t ) = 2.25 \pi t$ 
C)  $A \circ r ( t ) = 5.0625 t$ 
D)  $A \circ r ( t ) = 5.0625 \sqrt { t }$ 
E)  $A \circ r ( t ) = 5.0625 \pi t$ 
A)  $A \circ r ( t ) = 5.0625 \pi \sqrt { t }$ 
B)  $A \circ r ( t ) = 2.25 \pi t$ 
C)  $A \circ r ( t ) = 5.0625 t$ 
D)  $A \circ r ( t ) = 5.0625 \sqrt { t }$ 
E)  $A \circ r ( t ) = 5.0625 \pi t$ E

Question 4

The weekly cost C of producing units x in a manufacturing process is given by $C ( x ) = 30 x + 750$ .The number of units x produced in t hours is given by $x ( t ) = 70 t$ . ​
Find the cost of the units produced in 6 hours.
​

Accepted Answer

A) 11,855 
B) 11,850 
C) 11,846 
D) 13,350 
E) 11,854 
A) 11,855 
B) 11,850 
C) 11,846 
D) 13,350 
E) 11,854

Question 5

Find ( f − g )(x).​ $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

Accepted Answer

A)  $( f - g ) ( x ) = \frac { - 6 x + 34 } { 7 x - 6 }$ 
B)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x + 24 } { 7 x ^ { 2 } - 6 x }$ 
C)  $( f - g ) ( x ) = \frac { - 3 x + 2 } { 3 x - 3 }$ 
D)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x - 24 } { 7 x ^ { 2 } - 6 x }$ 
E)  $( f - g ) ( x ) = \frac { - 6 x + 22 } { 7 x - 6 }$ 
A)  $( f - g ) ( x ) = \frac { - 6 x + 34 } { 7 x - 6 }$ 
B)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x + 24 } { 7 x ^ { 2 } - 6 x }$ 
C)  $( f - g ) ( x ) = \frac { - 3 x + 2 } { 3 x - 3 }$ 
D)  $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x - 24 } { 7 x ^ { 2 } - 6 x }$ 
E)  $( f - g ) ( x ) = \frac { - 6 x + 22 } { 7 x - 6 }$

Question 6

​Find $g \circ f$ .​ $f ( x ) = x ^ { 2 } , g ( x ) = x - 4$ ​ ​

Accepted Answer

A)  $x ^ { 2 } - 4$ 
B)  $x ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  $\left( x ^ { 2 } + 4 \right)$ 
E)  $( x + 4 ) ^ { 2 }$ 
A)  $x ^ { 2 } - 4$ 
B)  $x ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  $\left( x ^ { 2 } + 4 \right)$ 
E)  $( x + 4 ) ^ { 2 }$

Question 7

Let f (x)= 3x,g (x)= x + 1.Find the composite function. ​​ $( f \circ g ) ( x )$ ​
Please give the respnce as an expression (not an equation).

Accepted Answer

The answer of Let f (x)= 3x,g (x)= x +...

Question 8

The total numbers of Navy personnel N (in thousands)and Marines personnel M (in thousands)from 2000 through 2007 can be approximated by the models​ $N ( t ) = 0.194 t ^ { 3 } - 7.88 t ^ { 2 } + 12.9 t + 375$ and $M ( t ) = 0.031 t ^ { 3 } - 0.25 t ^ { 2 } + 6.7 t + 173$ ​ where t represents the year,with t = 0 corresponding to 2000.
Find and interpret $( N - M ) ( t )$ .
​

Accepted Answer

A)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
B)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t - 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
C)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
D)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
E)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
A)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
B)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t - 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
C)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
D)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel. 
E)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.

Question 9

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = | x | , g ( x ) = x + 3$ ​

Accepted Answer

A)  $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x 
B)  $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x 
C)  $| x + 3 |$ Domain of $f \circ g$ : all real numbers x 
D)  $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x 
E)  $| x - 3 |$ Domain of $f \circ g$ : all real numbers x 
A)  $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x 
B)  $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x 
C)  $| x + 3 |$ Domain of $f \circ g$ : all real numbers x 
D)  $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x 
E)  $| x - 3 |$ Domain of $f \circ g$ : all real numbers x

Question 10

Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$ ​

Accepted Answer

A)  $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
B)  $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
C)  $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x 
D)  $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
E)  $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
A)  $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
B)  $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
C)  $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x 
D)  $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
E)  $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Question 11

​Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 2$ .​ $( f g ) ( 5 )$ ​ ​

Accepted Answer

A) 92 
B) 90 
C) -86 
D) 89 
E) 91 
A) 92 
B) 90 
C) -86 
D) 89 
E) 91

Question 12

The number of people playing tennis T (in millions)in the United States from 2000 through 2007 can be approximated by the function​ $T ( t ) = 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8$ ​ and the U.S.population P (in millions)from 2000 through 2007 can be approximated by the function $P ( t ) = 5.78 t + 221.5$ ,where t represents the year,with t = 0 corresponding to 2000.
Find $h ( t ) = \frac { T ( t ) } { P ( t ) }$ .
​

Accepted Answer

A)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​ 
B)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​ 
C)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t - 26.8 } { 5.78 t - 221.5 }$ 
D)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t - 221.5 }$ ​ 
E)  $h ( t ) = \frac { 0.0236 t ^ { 4 } + 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ 
A)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​ 
B)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​ 
C)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t - 26.8 } { 5.78 t - 221.5 }$ 
D)  $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t - 221.5 }$ ​ 
E)  $h ( t ) = \frac { 0.0236 t ^ { 4 } + 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$

Question 13

The monthly cost C of running the machinery in a factory for t hours is given by​ $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

Accepted Answer

A)  $C ( x ) = 46 x + 440$ 
B)  $C ( x ) = 240 x + 16,000$ 
C)  $C ( x ) = 40 x + 406$ 
D)  $C ( x ) = 46 x + 400$ 
E)  $C ( x ) = 240 x + 400$ ​ 
A)  $C ( x ) = 46 x + 440$ 
B)  $C ( x ) = 240 x + 16,000$ 
C)  $C ( x ) = 40 x + 406$ 
D)  $C ( x ) = 46 x + 400$ 
E)  $C ( x ) = 240 x + 400$ ​

Question 14

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

Accepted Answer

A) 15 
B) -35 
C) -23 
D) -25 
E) -33 
A) 15 
B) -35 
C) -23 
D) -25 
E) -33

Question 15

Find $( f g ) ( x )$ .​ $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$ ​

Accepted Answer

A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 2 } }$ 
C)  $\frac { 1 } { x ^ { 6 } }$ 
D)  $x ^ { 6 }$ 
E)  $\frac { x ^ { 4 } } { x ^ { 2 } }$ 
A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 2 } }$ 
C)  $\frac { 1 } { x ^ { 6 } }$ 
D)  $x ^ { 6 }$ 
E)  $\frac { x ^ { 4 } } { x ^ { 2 } }$

Question 16

The number N of bacteria in a refrigerated food is given by $N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20$ where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration,the temperature of the food is given by $T ( t ) = 3 t + 2,0 \leq t \leq 6$ where t is the time in hours. Find the bacteria count after 0.5 hour.
​

Accepted Answer

A) About 565 bacteria 
B) About 793 bacteria 
C) About 653 bacteria 
D) About 390 bacteria 
E) About 705 bacteria 
A) About 565 bacteria 
B) About 793 bacteria 
C) About 653 bacteria 
D) About 390 bacteria 
E) About 705 bacteria

Question 17

Find $( f / g ) ( x )$ .​ $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$ ​

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 6 }$ 
C)  $\frac { 1 } { x ^ { 4 } }$ ​ 
D)  $\frac { 1 } { x ^ { 6 } }$ 
E)  $x ^ { 2 }$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 6 }$ 
C)  $\frac { 1 } { x ^ { 4 } }$ ​ 
D)  $\frac { 1 } { x ^ { 6 } }$ 
E)  $x ^ { 2 }$

Question 18

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

Accepted Answer

A)  $( f \circ g ) ( x ) = - 2 x - 19$ 
B)  $( f \circ g ) ( x ) = - 3 x - 14$ 
C)  $( f \circ g ) ( x ) = - 2 x ^ { 2 } - 19 x - 45$ 
D)  $( f \circ g ) ( x ) = - 3 x - 4$ 
E)  $( f \circ g ) ( x ) = - 2 x - 4$ 
A)  $( f \circ g ) ( x ) = - 2 x - 19$ 
B)  $( f \circ g ) ( x ) = - 3 x - 14$ 
C)  $( f \circ g ) ( x ) = - 2 x ^ { 2 } - 19 x - 45$ 
D)  $( f \circ g ) ( x ) = - 3 x - 4$ 
E)  $( f \circ g ) ( x ) = - 2 x - 4$

Question 19

Let f (x)= x2 - 1,g (x)= 3x - 2.Find the value of the function.​ $( f + g ) ( 5 )$

Accepted Answer

Question 20

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ .​ $( f - g ) ( 3 t )$ ​ ​

Accepted Answer

A)  $9 t ^ { 2 } + 3 t + 7$ 
B)  $6 t + 7$ 
C)  $9 t ^ { 2 } + 3 t - 7$ 
D)  $9 t ^ { 2 } - 3 t - 7$ 
E)  $9 t ^ { 2 } - 3 t + 7$ 
A)  $9 t ^ { 2 } + 3 t + 7$ 
B)  $6 t + 7$ 
C)  $9 t ^ { 2 } + 3 t - 7$ 
D)  $9 t ^ { 2 } - 3 t - 7$ 
E)  $9 t ^ { 2 } - 3 t + 7$

Exam 8: Combinations of Functions Composite Functions

Determine whether the statement is true or false. ​ If f(x)= x + 1 and g(x)= 5x,then (f∘g)(x)=(g∘f)(x)( f \circ g ) ( x ) = ( g \circ f ) ( x )(f∘g)(x)=(g∘f)(x) . ​

Let f (x)= 2x + 1,g(x)= 3x - 2.Find the function.​ (f−g)(x)( f - g ) ( x )(f−g)(x) ​

The weekly cost C of producing units x in a manufacturing process is given by C(x)=30x+750C ( x ) = 30 x + 750C(x)=30x+750 .The number of units x produced in t hours is given by x(t)=70tx ( t ) = 70 tx(t)=70t . ​ Find the cost of the units produced in 6 hours. ​

Find ( f − g )(x).​ f(x)=−6x7x−6g(x)=−4xf ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }f(x)=−7x−66x​g(x)=−x4​

​Find g∘fg \circ fg∘f .​ f(x)=x2,g(x)=x−4f ( x ) = x ^ { 2 } , g ( x ) = x - 4f(x)=x2,g(x)=x−4 ​ ​

Let f (x)= 3x,g (x)= x + 1.Find the composite function. ​​ (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) ​ Please give the respnce as an expression (not an equation).

Find f∘gf \circ gf∘g and the domain of the composite function.​ f(x)=∣x∣,g(x)=x+3f ( x ) = | x | , g ( x ) = x + 3f(x)=∣x∣,g(x)=x+3 ​

Find g∘fg \circ fg∘f and the domain of the composite function.​ f(x)=x2+4,g(x)=xf ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }f(x)=x2+4,g(x)=x​ ​

​Evaluate the indicated function for f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 and g(x)=x−2g ( x ) = x - 2g(x)=x−2 .​ (fg)(5)( f g ) ( 5 )(fg)(5) ​ ​

The monthly cost C of running the machinery in a factory for t hours is given by​ C(t)=40t+400C ( t ) = 40 t + 400C(t)=40t+400 The number of hours t needed to produce x products is given by t(x)=6xt ( x ) = 6 xt(x)=6x . Find the equation representing the cost C of manufacturing x products.

Evaluate the indicated function for f(x)=x2−6f ( x ) = x ^ { 2 } - 6f(x)=x2−6 and g(x)=x+4g ( x ) = x + 4g(x)=x+4 . ( fg )(1)

Find (fg)(x)( f g ) ( x )(fg)(x) .​ f(x)=1x2,g(x)=1x4f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }f(x)=x21​,g(x)=x41​ ​

Find (f/g)(x)( f / g ) ( x )(f/g)(x) .​ f(x)=1x2,g(x)=1x4f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }f(x)=x21​,g(x)=x41​ ​

Find f∘gf \circ gf∘g . f(x)=−2x−9g(x)=x+5f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5f(x)=−2x−9g(x)=x+5

Let f (x)= x2 - 1,g (x)= 3x - 2.Find the value of the function.​ (f+g)(5)( f + g ) ( 5 )(f+g)(5)

Evaluate the indicated function for f(x)=x2+3f ( x ) = x ^ { 2 } + 3f(x)=x2+3 and g(x)=x−4g ( x ) = x - 4g(x)=x−4 .​ (f−g)(3t)( f - g ) ( 3 t )(f−g)(3t) ​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Determine whether the statement is true or false. If f(x)= x + 1 and g(x)= 5x,then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .

Let f (x)= 2x + 1,g(x)= 3x - 2.Find the function. $( f - g ) ( x )$

The weekly cost C of producing units x in a manufacturing process is given by $C ( x ) = 30 x + 750$ .The number of units x produced in t hours is given by $x ( t ) = 70 t$ . Find the cost of the units produced in 6 hours.

Find ( f − g )(x). $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

Find $g \circ f$ . $f ( x ) = x ^ { 2 } , g ( x ) = x - 4$

Let f (x)= 3x,g (x)= x + 1.Find the composite function. $( f \circ g ) ( x )$ Please give the respnce as an expression (not an equation).

Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

Find $g \circ f$ and the domain of the composite function. $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 2$ . $( f g ) ( 5 )$

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

Find $( f g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

Find $( f / g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

Let f (x)= x² - 1,g (x)= 3x - 2.Find the value of the function. $( f + g ) ( 5 )$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ . $( f - g ) ( 3 t )$