Question 1

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 7$ and $g ( x ) = x + 8$ .​ $( f - g ) ( t + 8 )$

Accepted Answer

A) ​ $t ^ { 2 } + 15 t + 57$ 
B) ​ $t ^ { 2 } + 15 t + 41$ 
C) ​ $t ^ { 2 } + 17 t + 41$ 
D) ​ $t ^ { 2 } - t + 41$ 
E) ​ $t ^ { 2 } + 17 t + 57$ 
A) ​ $t ^ { 2 } + 15 t + 57$ 
B) ​ $t ^ { 2 } + 15 t + 41$ 
C) ​ $t ^ { 2 } + 17 t + 41$ 
D) ​ $t ^ { 2 } - t + 41$ 
E) ​ $t ^ { 2 } + 17 t + 57$

Question 2

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

Accepted Answer

A)  $( f g ) ( x ) = \sqrt { 8 x + 7 }$ 
B)  $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 7 }$ 
C)  $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 21 x }$ 
D)  $( f g ) ( x ) = x \sqrt { 15 } + \sqrt { 21 x }$ 
E)  $( f g ) ( x ) = x \sqrt { 15 + 21 x }$ 
A)  $( f g ) ( x ) = \sqrt { 8 x + 7 }$ 
B)  $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 7 }$ 
C)  $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 21 x }$ 
D)  $( f g ) ( x ) = x \sqrt { 15 } + \sqrt { 21 x }$ 
E)  $( f g ) ( x ) = x \sqrt { 15 + 21 x }$

Question 3

The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident,the distance (in feet)the car travels during the driver's reaction time is given by $R ( x ) = \frac { 5 } { 2 } x$ ,where x is the speed of the car in miles per hour.The distance (in feet)traveled while the driver is braking is given by $B ( x ) = \frac { 1 } { 11 } x ^ { 2 }$ .Find the function that represents the total stopping distance T. ​

Accepted Answer

A)  $T = - \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
B)  $T = \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
C)  $T = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 11 } x ^ { 2 }$ 
D)  $T = - \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
E)  $T = \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
A)  $T = - \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
B)  $T = \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
C)  $T = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 11 } x ^ { 2 }$ 
D)  $T = - \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
E)  $T = \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$

Question 4

Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = | x | , g ( x ) = x + 4$ ​ ​

Accepted Answer

A)  $| x - 4 |$ Domain of $g \circ f$ : all real numbers x 
B)  $x - | 4 |$ Domain of $g \circ f$ : all real numbers x 
C)  $| x | - 4$ Domain of $g \circ f$ : all real numbers x 
D)  $| x | + 4$ Domain of $g \circ f$ : all real numbers x 
E)  $| x + 4 |$ Domain of $g \circ f$ : all real numbers x 
A)  $| x - 4 |$ Domain of $g \circ f$ : all real numbers x 
B)  $x - | 4 |$ Domain of $g \circ f$ : all real numbers x 
C)  $| x | - 4$ Domain of $g \circ f$ : all real numbers x 
D)  $| x | + 4$ Domain of $g \circ f$ : all real numbers x 
E)  $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Question 5

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

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - \infty , 0 ]$ 
D)  $( - \infty , 0 )$ 
E)  $( 0 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - \infty , 0 ]$ 
D)  $( - \infty , 0 )$ 
E)  $( 0 , \infty )$

Question 6

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 .
​
Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.
​

Accepted Answer

A)  $R ( p ) = 2000 - p$ 
B)  $R ( p ) = p - 2000$ 
C)  $R ( p ) = p + 2000$ 
D)  $R ( p ) = p + 1000$ 
E)  $R ( p ) = p - 1000$ 
A)  $R ( p ) = 2000 - p$ 
B)  $R ( p ) = p - 2000$ 
C)  $R ( p ) = p + 2000$ 
D)  $R ( p ) = p + 1000$ 
E)  $R ( p ) = p - 1000$

Question 7

Find (f + g)(x).​ $$f ( x ) = x + 4 , g ( x ) = x - 4$$ ​

Accepted Answer

A) 2x 
B) 4x 
C) -4x 
D) -2x 
E) 2x + 8 
A) 2x 
B) 4x 
C) -4x 
D) -2x 
E) 2x + 8

Question 8

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$ ​

Accepted Answer

A)  $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x 
B)  $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x 
C)  $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x 
D)  $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x 
E)  $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x 
A)  $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x 
B)  $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x 
C)  $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x 
D)  $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x 
E)  $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x

Question 9

Find (f + g)(x).​​ $\begin{array} { l } 
f ( x ) = x ^ { 2 } - 2 x - 1 \
g ( x ) = - 3 x ^ { 2 } + x - 1
\end{array}$ ​ ​

Accepted Answer

A) ​ $( f + g ) ( x ) = 4 x ^ { 4 } - 3 x ^ { 2 }$ 
B) ​ $( f + g ) ( x ) = 2 x ^ { 2 } - x + 2$ 
C) ​ $( f + g ) ( x ) = - 2 x ^ { 4 } - x ^ { 2 } - 2$ 
D) ​ $( f + g ) ( x ) = 4 x ^ { 2 } - 3 x$ 
E) ​ $( f + g ) ( x ) = - 2 x ^ { 2 } - x - 2$ 
A) ​ $( f + g ) ( x ) = 4 x ^ { 4 } - 3 x ^ { 2 }$ 
B) ​ $( f + g ) ( x ) = 2 x ^ { 2 } - x + 2$ 
C) ​ $( f + g ) ( x ) = - 2 x ^ { 4 } - x ^ { 2 } - 2$ 
D) ​ $( f + g ) ( x ) = 4 x ^ { 2 } - 3 x$ 
E) ​ $( f + g ) ( x ) = - 2 x ^ { 2 } - x - 2$

Question 10

Find (fg)(x).​ $$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$$ ​

Accepted Answer

A)  $$7 x ^ { 3 } + 7 x ^ { 2 }$$ 
B)  $7 x ^ { 3 } - 7 x ^ { 2 }$ 
C)  $7 x ^ { 2 } - 7 x ^ { 3 }$ 
D)  $7 x ^ { 2 } + 7 x ^ { 3 }$ 
E)  $7 x - 7 x ^ { 2 }$ 
A)  $$7 x ^ { 3 } + 7 x ^ { 2 }$$ 
B)  $7 x ^ { 3 } - 7 x ^ { 2 }$ 
C)  $7 x ^ { 2 } - 7 x ^ { 3 }$ 
D)  $7 x ^ { 2 } + 7 x ^ { 3 }$ 
E)  $7 x - 7 x ^ { 2 }$

Question 11

​Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ ​

Accepted Answer

A)  $\frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 5$ 
B)  $\frac { 1 } { x } - 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$ 
C)  $\frac { 1 } { x } + 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$ 
D)  $- \frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 3$ 
E)  $\frac { 1 } { x - 5 }$ Domain of $g \circ f$ : all real numbers x except $x = 5$ 
A)  $\frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 5$ 
B)  $\frac { 1 } { x } - 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$ 
C)  $\frac { 1 } { x } + 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$ 
D)  $- \frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 3$ 
E)  $\frac { 1 } { x - 5 }$ Domain of $g \circ f$ : all real numbers x except $x = 5$

Question 12

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​ $N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$ and $M ( t ) = 0.033 t ^ { 3 } - 0.21 t ^ { 2 } + 1.7 t + 171$ ​ where t represents the year,with t = 0 corresponding to 2000.
​
Find and interpret $( N + M ) ( t )$ .
​

Accepted Answer

A)  $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined. 
B)  $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined. 
C)  $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined. 
D)  $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined. 
E)  $( N + M ) ( t ) = 0.226 t ^ { 2 } - 4.09 t ^ { 3 } - 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined. 
A)  $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined. 
B)  $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined. 
C)  $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined. 
D)  $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined. 
E)  $( N + M ) ( t ) = 0.226 t ^ { 2 } - 4.09 t ^ { 3 } - 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined.

Question 13

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 6$ .​ $( f - g ) ( - 5 )$ ​ ​

Accepted Answer

A) 28 
B) 38 
C) -38 
D) 125 
E) 17 
A) 28 
B) 38 
C) -38 
D) 125 
E) 17

Question 14

Find $f \circ g$ .​ $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$ ​

Accepted Answer

A)  $$( f \circ g ) ( x ) = \left| x ^ { 2 } - 18 x + 82 \right|$$ 
B)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 82 \right|$ 
C)  $( f \circ g ) ( x ) = \left| 8 - x ^ { 2 } \right|$ 
D)  $( f \circ g ) ( x ) = \left| 10 - x ^ { 2 } \right|$ 
E)  $$( f \circ g ) ( x ) = 9 - \left| x ^ { 2 } + 1 \right|$$ 
A)  $$( f \circ g ) ( x ) = \left| x ^ { 2 } - 18 x + 82 \right|$$ 
B)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 82 \right|$ 
C)  $( f \circ g ) ( x ) = \left| 8 - x ^ { 2 } \right|$ 
D)  $( f \circ g ) ( x ) = \left| 10 - x ^ { 2 } \right|$ 
E)  $$( f \circ g ) ( x ) = 9 - \left| x ^ { 2 } + 1 \right|$$

Question 15

Find (f + g)(x).​ $$f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$$ ​

Accepted Answer

A)  $$x ^ { 2 } + 4 - \sqrt { 7 - x }$$ 
B)  $x ^ { 2 } + 4 + \sqrt { 7 - x }$ 
C)  $x ^ { 2 } - 4 + \sqrt { 7 + x }$ 
D)  $x ^ { 2 } - 4 - \sqrt { 7 - x }$ 
E)  $x ^ { 2 } - 4 + \sqrt { 7 - x }$ 
A)  $$x ^ { 2 } + 4 - \sqrt { 7 - x }$$ 
B)  $x ^ { 2 } + 4 + \sqrt { 7 - x }$ 
C)  $x ^ { 2 } - 4 + \sqrt { 7 + x }$ 
D)  $x ^ { 2 } - 4 - \sqrt { 7 - x }$ 
E)  $x ^ { 2 } - 4 + \sqrt { 7 - x }$

Question 16

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

Accepted Answer

A) 12 
B) -10 
C) 7 
D) 14 
E) 10 
A) 12 
B) -10 
C) 7 
D) 14 
E) 10

Question 17

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ .Find the composite function.​ $( f \circ g ) ( x )$

Accepted Answer

The answer of Let \(f ( x ) = \sqrt...

Question 18

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$ ​

Accepted Answer

A)  $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
B)  $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
C)  $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
D)  $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
E)  $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$ 
A)  $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
B)  $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
C)  $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
D)  $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
E)  $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$

Exam 8: Combinations of Functions Composite Functions

Evaluate the indicated function for f(x)=x2−7f ( x ) = x ^ { 2 } - 7f(x)=x2−7 and g(x)=x+8g ( x ) = x + 8g(x)=x+8 .​ (f−g)(t+8)( f - g ) ( t + 8 )(f−g)(t+8)

Find ( fg )(x). f(x)=3xg(x)=5x+7f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }f(x)=3x​g(x)=5x+7​

Find g∘fg \circ fg∘f and the domain of the composite function.​ f(x)=∣x∣,g(x)=x+4f ( x ) = | x | , g ( x ) = x + 4f(x)=∣x∣,g(x)=x+4 ​ ​

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

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 . ​ Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory. ​

Find (f + g)(x).​ f(x)=x+4,g(x)=x−4f ( x ) = x + 4 , g ( x ) = x - 4f(x)=x+4,g(x)=x−4 ​

Find f∘gf \circ gf∘g and the domain of the composite function.​ f(x)=x+5,g(x)=x2f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }f(x)=x+5​,g(x)=x2 ​

Find (f + g)(x).​​ f(x)=-2x-1 g(x)=-3+x-1 ​ ​

Find (fg)(x).​ f(x)=x2,g(x)=7x−7f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7f(x)=x2,g(x)=7x−7 ​

​Find g∘fg \circ fg∘f and the domain of the composite function.​ f(x)=1x,g(x)=x+5f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5f(x)=x1​,g(x)=x+5 ​

Evaluate the indicated function for f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2 and g(x)=x−6g ( x ) = x - 6g(x)=x−6 .​ (f−g)(−5)( f - g ) ( - 5 )(f−g)(−5) ​ ​

Find f∘gf \circ gf∘g .​ f(x)=∣x2+1∣g(x)=9−xf ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - xf(x)=​x2+1​g(x)=9−x ​

Find (f + g)(x).​ f(x)=x2+4,g(x)=7−xf ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }f(x)=x2+4,g(x)=7−x​ ​

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

Let f(x)=x+1,g(x)=x2−1f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1f(x)=x+1​,g(x)=x2−1 .Find the composite function.​ (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Find f∘gf \circ gf∘g and the domain of the composite function.​ f(x)=1x,g(x)=x+7f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7f(x)=x1​,g(x)=x+7 ​

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

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 7$ and $g ( x ) = x + 8$ . $( f - g ) ( t + 8 )$

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

Find $g \circ f$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 4$

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

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 . Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.

Find (f + g)(x). $f ( x ) = x + 4 , g ( x ) = x - 4$

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

Find (f + g)(x). f(x)=-2x-1 g(x)=-3+x-1

Find (fg)(x). $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$

Find $g \circ f$ and the domain of the composite function. $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 6$ . $( f - g ) ( - 5 )$

Find $f \circ g$ . $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$

Find (f + g)(x). $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$

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

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ .Find the composite function. $( f \circ g ) ( x )$

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$