Question 1

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = 4 x - 3$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 3 } { 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 } + 3$ 
C)  Not a one-to-one function 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 4 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x + 3 } { 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 } + 3$ 
C)  Not a one-to-one function 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 4 }$ A

Question 2

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:
  
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year $2002 .$

Accepted Answer

A)  About $\$ 1,000,000$ 
B)  About $\$ 1,700,000$ 
C)  About $\$ 750,000$ 
D)  About $\$ 1,300,000$ 
A)  About $\$ 1,000,000$ 
B)  About $\$ 1,700,000$ 
C)  About $\$ 750,000$ 
D)  About $\$ 1,300,000$ D

Question 3

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$$

Accepted Answer

A) True 
 B)False  True

Question 4

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = \frac { x ^ { 5 } - 3 } { x ^ { 5 } + 2 }$$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 2 , g ( x ) = x ^ { 5 } - 3$ 
B)  $f ( x ) = x ^ { 5 } , g ( x ) = \frac { x - 3 } { x + 2 }$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 5 } + 2 } , g ( x ) = x ^ { 5 } - 3$ 
D)  $f ( x ) = \frac { x - 3 } { x + 2 } , g ( x ) = x ^ { 5 }$ 
A)  $f ( x ) = x ^ { 5 } + 2 , g ( x ) = x ^ { 5 } - 3$ 
B)  $f ( x ) = x ^ { 5 } , g ( x ) = \frac { x - 3 } { x + 2 }$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 5 } + 2 } , g ( x ) = x ^ { 5 } - 3$ 
D)  $f ( x ) = \frac { x - 3 } { x + 2 } , g ( x ) = x ^ { 5 }$

Question 5

Find the requested composition of functions.
-Given $f ( x ) = \frac { x - 9 } { 7 }$ and $g ( x ) = 7 x + 9$, find $g \circ f ( x )$

Accepted Answer

A)  $x$ 
B)  $x + 18$ 
C)  $x - \frac { 9 } { 7 }$ 
D)  $7 x + 54$ 
A)  $x$ 
B)  $x + 18$ 
C)  $x - \frac { 9 } { 7 }$ 
D)  $7 x + 54$

Question 6

Find the requested composition of functions.
-Given $f ( x ) = \frac { 5 } { x }$ and $g ( x ) = 2 x ^ { 3 }$, find $g \circ f ( x )$

Accepted Answer

A)  $\frac { 2 x ^ { 3 } } { 125 }$ 
B)  $\frac { 250 } { x ^ { 3 } }$ 
C)  $\frac { 5 } { 2 x ^ { 3 } }$ 
D)  $\frac { 2 x ^ { 3 } } { 5 }$ 
A)  $\frac { 2 x ^ { 3 } } { 125 }$ 
B)  $\frac { 250 } { x ^ { 3 } }$ 
C)  $\frac { 5 } { 2 x ^ { 3 } }$ 
D)  $\frac { 2 x ^ { 3 } } { 5 }$

Question 7

Graph the function as a solid curve and its inverse as a dashed curve.
-f(x)= 5x

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = 9 x - 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 9 } x + 1$$

Accepted Answer

A) True 
 B)False

Question 9

Solve the problem.
-A size $- 2$ dress in Country $\mathrm { C }$ is size $- 20$ in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x - 22$. Find a formula for the inverse of the function described.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 22$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 22 }$ 
C)  $f ^ { - 1 } ( x ) = x - 22$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { - 22 }$ 
A)  $f ^ { - 1 } ( x ) = x + 22$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 22 }$ 
C)  $f ^ { - 1 } ( x ) = x - 22$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { - 22 }$

Question 10

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = \sqrt [ 3 ] { x + 2 }$$

Accepted Answer

A)  Not a one-to-one function 
B)  $f ^ { - 1 } ( x ) = ( x + 2 ) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 2$ 
A)  Not a one-to-one function 
B)  $f ^ { - 1 } ( x ) = ( x + 2 ) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 2$

Question 11

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = ( x - 9 ) ^ { 2 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x + 9 } }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } + 9$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$ 
D)  Not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x + 9 } }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } + 9$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$ 
D)  Not a one-to-one function

Question 12

Find the requested composition of functions.
-Given $f ( x ) = 6 x ^ { 2 } - 4$ and $g ( x ) = \frac { 5 } { x }$, find $f \circ g ( x )$

Accepted Answer

A)  $\frac { 150 } { x } - 4$ 
B)  $\frac { 150 } { x ^ { 2 } } - 4$ 
C)  $30 x - \frac { 20 } { x }$ 
D)  $\frac { 5 } { 6 x ^ { 2 } - 4 }$ 
A)  $\frac { 150 } { x } - 4$ 
B)  $\frac { 150 } { x ^ { 2 } } - 4$ 
C)  $30 x - \frac { 20 } { x }$ 
D)  $\frac { 5 } { 6 x ^ { 2 } - 4 }$

Question 13

Find an equation of the inverse of the relation.
-y = 2 + 6x

Accepted Answer

A) y = 6 - 2x 
B) x = 6 + 2y 
C) y = 6 + 2x 
D) x = 2 + 6y 
A) y = 6 - 2x 
B) x = 6 + 2y 
C) y = 6 + 2x 
D) x = 2 + 6y

Question 14

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table: 
 
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year $2002 .$

Accepted Answer

A)  About $\$ 500,000$ 
B)  About $\$ 900,000$ 
C)  About $\$ 800,000$ 
D)  About $\$ 1,000,000$ 
A)  About $\$ 500,000$ 
B)  About $\$ 900,000$ 
C)  About $\$ 800,000$ 
D)  About $\$ 1,000,000$

Question 15

Determine whether the function is one-to-one.
-$$f ( x ) = \left| 25 - x ^ { 2 } \right|$$

Accepted Answer

A) True 
 B)False

Question 16

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = \frac { 3 } { x + 7 } , f ^ { - 1 } ( x ) = \frac { 7 x + 3 } { x }$$

Accepted Answer

A) True 
 B)False

Question 17

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$h ( x ) = \sqrt { - 81 x ^ { 2 } + 71 }$

Accepted Answer

A)  $f ( x ) = \sqrt { - 81 x + 71 } , g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = \sqrt { x } , g ( x ) = - 81 x ^ { 2 } + 71$ 
C)  $f ( x ) = \sqrt { - 81 x ^ { 2 } } , g ( x ) = \sqrt { 71 }$ 
D)  $f ( x ) = - 81 x ^ { 2 } + 71 , g ( x ) = \sqrt { x }$ 
A)  $f ( x ) = \sqrt { - 81 x + 71 } , g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = \sqrt { x } , g ( x ) = - 81 x ^ { 2 } + 71$ 
C)  $f ( x ) = \sqrt { - 81 x ^ { 2 } } , g ( x ) = \sqrt { 71 }$ 
D)  $f ( x ) = - 81 x ^ { 2 } + 71 , g ( x ) = \sqrt { x }$

Question 18

Determine whether the function is one-to-one.
-$$f ( x ) = 3 x ^ { 3 } - 8$$

Accepted Answer

A) True 
 B)False

Question 19

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = 5 x + 4 \mid$$

Accepted Answer

A)  $f ( x ) = x , g ( x ) = 5 x + 4$ 
B)  $f ( x ) = | - x | , g ( x ) = 5 x - 4$ 
C)  $f ( x ) = | x | , g ( x ) = 5 x + 4$ 
D)  $f ( x ) = - | x | , g ( x ) = 5 x + 4$ 
A)  $f ( x ) = x , g ( x ) = 5 x + 4$ 
B)  $f ( x ) = | - x | , g ( x ) = 5 x - 4$ 
C)  $f ( x ) = | x | , g ( x ) = 5 x + 4$ 
D)  $f ( x ) = - | x | , g ( x ) = 5 x + 4$

Question 20

Solve the problem.
-A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = \frac { x } { 2 } - 8$. Find a formula for the inverse of the function described.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = 2 ( x - 8 )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 2 \mathrm { x } + 8$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8$ 
D)  $f ^ { - 1 } ( x ) = 2 ( x + 8 )$ 
A)  $f ^ { - 1 } ( x ) = 2 ( x - 8 )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 2 \mathrm { x } + 8$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8$ 
D)  $f ^ { - 1 } ( x ) = 2 ( x + 8 )$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 4 x - 3$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { x ^ { 5 } - 3 } { x ^ { 5 } + 2 }$

Find the requested composition of functions. -Given $f ( x ) = \frac { x - 9 } { 7 }$ and $g ( x ) = 7 x + 9$ , find $g \circ f ( x )$

Find the requested composition of functions. -Given $f ( x ) = \frac { 5 } { x }$ and $g ( x ) = 2 x ^ { 3 }$ , find $g \circ f ( x )$

Graph the function as a solid curve and its inverse as a dashed curve. -f(x)= 5x

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 9 x - 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 9 } x + 1$

Solve the problem. -A size $- 2$ dress in Country $\mathrm { C }$ is size $- 20$ in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x - 22$ . Find a formula for the inverse of the function described.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \sqrt [ 3 ] { x + 2 }$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = ( x - 9 ) ^ { 2 }$

Find the requested composition of functions. -Given $f ( x ) = 6 x ^ { 2 } - 4$ and $g ( x ) = \frac { 5 } { x }$ , find $f \circ g ( x )$

Find an equation of the inverse of the relation. -y = 2 + 6x

Determine whether the function is one-to-one. - $f ( x ) = \left| 25 - x ^ { 2 } \right|$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = \frac { 3 } { x + 7 } , f ^ { - 1 } ( x ) = \frac { 7 x + 3 } { x }$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \sqrt { - 81 x ^ { 2 } + 71 }$

Determine whether the function is one-to-one. - $f ( x ) = 3 x ^ { 3 } - 8$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = 5 x + 4 \mid$

Solve the problem. -A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = \frac { x } { 2 } - 8$ . Find a formula for the inverse of the function described.

Introduction to Real Numbers and Algebraic Expressions

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Graphs of Linear Equations

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Exam 12: Exponential Functions and Logarithmic Functions

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=4x−3f ( x ) = 4 x - 3f(x)=4x−3

Use composition to verify whether or not the inverse is correct. - f(x)=−18x,f−1(x)=−8xf ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 xf(x)=−81​x,f−1(x)=−8x

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=x5−3x5+2h ( x ) = \frac { x ^ { 5 } - 3 } { x ^ { 5 } + 2 }h(x)=x5+2x5−3​

Find the requested composition of functions. -Given f(x)=x−97f ( x ) = \frac { x - 9 } { 7 }f(x)=7x−9​ and g(x)=7x+9g ( x ) = 7 x + 9g(x)=7x+9 , find g∘f(x)g \circ f ( x )g∘f(x)

Find the requested composition of functions. -Given f(x)=5xf ( x ) = \frac { 5 } { x }f(x)=x5​ and g(x)=2x3g ( x ) = 2 x ^ { 3 }g(x)=2x3 , find g∘f(x)g \circ f ( x )g∘f(x)

Graph the function as a solid curve and its inverse as a dashed curve. -f(x)= 5x

Use composition to verify whether or not the inverse is correct. - f(x)=9x−9,f−1(x)=19x+1f ( x ) = 9 x - 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 9 } x + 1f(x)=9x−9,f−1(x)=91​x+1

Solve the problem. -A size −2- 2−2 dress in Country C\mathrm { C }C is size −20- 20−20 in Country D. A function that converts dress sizes in Country C to those in Country DDD is f(x)=x−22f ( x ) = x - 22f(x)=x−22 . Find a formula for the inverse of the function described.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=x+23f ( x ) = \sqrt [ 3 ] { x + 2 }f(x)=3x+2​

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=(x−9)2f ( x ) = ( x - 9 ) ^ { 2 }f(x)=(x−9)2

Find the requested composition of functions. -Given f(x)=6x2−4f ( x ) = 6 x ^ { 2 } - 4f(x)=6x2−4 and g(x)=5xg ( x ) = \frac { 5 } { x }g(x)=x5​ , find f∘g(x)f \circ g ( x )f∘g(x)

Find an equation of the inverse of the relation. -y = 2 + 6x

Determine whether the function is one-to-one. - f(x)=∣25−x2∣f ( x ) = \left| 25 - x ^ { 2 } \right|f(x)=​25−x2​

Use composition to verify whether or not the inverse is correct. - f(x)=3x+7,f−1(x)=7x+3xf ( x ) = \frac { 3 } { x + 7 } , f ^ { - 1 } ( x ) = \frac { 7 x + 3 } { x }f(x)=x+73​,f−1(x)=x7x+3​

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=−81x2+71h ( x ) = \sqrt { - 81 x ^ { 2 } + 71 }h(x)=−81x2+71​

Determine whether the function is one-to-one. - f(x)=3x3−8f ( x ) = 3 x ^ { 3 } - 8f(x)=3x3−8

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=5x+4∣h ( x ) = 5 x + 4 \midh(x)=5x+4∣

Solve the problem. -A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those in Country DDD is f(x)=x2−8f ( x ) = \frac { x } { 2 } - 8f(x)=2x​−8 . Find a formula for the inverse of the function described.

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

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Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 4 x - 3$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { x ^ { 5 } - 3 } { x ^ { 5 } + 2 }$

Find the requested composition of functions. -Given $f ( x ) = \frac { x - 9 } { 7 }$ and $g ( x ) = 7 x + 9$ , find $g \circ f ( x )$

Find the requested composition of functions. -Given $f ( x ) = \frac { 5 } { x }$ and $g ( x ) = 2 x ^ { 3 }$ , find $g \circ f ( x )$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 9 x - 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 9 } x + 1$

Solve the problem. -A size $- 2$ dress in Country $\mathrm { C }$ is size $- 20$ in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = x - 22$ . Find a formula for the inverse of the function described.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \sqrt [ 3 ] { x + 2 }$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = ( x - 9 ) ^ { 2 }$

Find the requested composition of functions. -Given $f ( x ) = 6 x ^ { 2 } - 4$ and $g ( x ) = \frac { 5 } { x }$ , find $f \circ g ( x )$

Determine whether the function is one-to-one. - $f ( x ) = \left| 25 - x ^ { 2 } \right|$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = \frac { 3 } { x + 7 } , f ^ { - 1 } ( x ) = \frac { 7 x + 3 } { x }$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \sqrt { - 81 x ^ { 2 } + 71 }$

Determine whether the function is one-to-one. - $f ( x ) = 3 x ^ { 3 } - 8$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = 5 x + 4 \mid$

Solve the problem. -A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = \frac { x } { 2 } - 8$ . Find a formula for the inverse of the function described.