Question 1

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

Accepted Answer

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

Question 2

Graph the relation using solid circles and the inverse using open circles.
-$\{ ( - 9,3 ) , ( 9 , - 3 ) , ( - 7 , - 1 ) , ( 7,1 ) \}$

Accepted Answer

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

Question 3

Graph.
-$x = 2 y$

Accepted Answer

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

Question 4

Find an equation of the inverse of the relation.
-$$y = 4 + 6 x$$

Accepted Answer

A)  $y = 6 - 4 x$ 
B)  $y = 6 + 4 x$ 
C)  $x = 6 + 4 y$ 
D)  $x = 4 + 6 y$ 
A)  $y = 6 - 4 x$ 
B)  $y = 6 + 4 x$ 
C)  $x = 6 + 4 y$ 
D)  $x = 4 + 6 y$

Question 5

Find f(x)and g(x)such that h(x)= (f ° g)(x).
-$$h ( x ) = \frac { 8 } { x ^ { 2 } } + 7$$

Accepted Answer

A)  $f ( x ) = \frac { 8 } { x ^ { 2 } } , g ( x ) = 7$ 
B)  $f ( x ) = x , g ( x ) = \frac { 8 } { x } + 7$ 
C)  $f ( x ) = x + 7 , g ( x ) = \frac { 8 } { x ^ { 2 } }$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 8 } { x } + 7$ 
A)  $f ( x ) = \frac { 8 } { x ^ { 2 } } , g ( x ) = 7$ 
B)  $f ( x ) = x , g ( x ) = \frac { 8 } { x } + 7$ 
C)  $f ( x ) = x + 7 , g ( x ) = \frac { 8 } { x ^ { 2 } }$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 8 } { x } + 7$

Question 6

Determine whether the function is one-to-one.
-$$f ( x ) = \left| 36 - x ^ { 2 } \right|$$

Accepted Answer

A) True 
 B)False

Question 7

Solve the problem.
-A computer is purchased for $\$ 4500$. Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V ( t ) = 4500 ( 0.77 ) ^ { t }$. Find the value of the computer after 6 years.

Accepted Answer

A)  $\$ 556.08$ 
B)  $\$ 20,790.00$ 
C)  $\$ 937.90$ 
D)  $\$ 722.18$ 
A)  $\$ 556.08$ 
B)  $\$ 20,790.00$ 
C)  $\$ 937.90$ 
D)  $\$ 722.18$

Question 8

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = ( x + 5 ) ^ { 2 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x - 5 } }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x - 5 } }$

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

Graph the relation using solid circles and the inverse using open circles. - $\{ ( - 9,3 ) , ( 9 , - 3 ) , ( - 7 , - 1 ) , ( 7,1 ) \}$ $Graph the relation using solid circles and the inverse using open circles. - \{ ( - 9,3 ) , ( 9 , - 3 ) , ( - 7 , - 1 ) , ( 7,1 ) \}$

Graph. - $x = 2 y$

Find an equation of the inverse of the relation. - $y = 4 + 6 x$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \frac { 8 } { x ^ { 2 } } + 7$

Determine whether the function is one-to-one. - $f ( x ) = \left| 36 - x ^ { 2 } \right|$

Solve the problem. -A computer is purchased for $\$ 4500$ . Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V ( t ) = 4500 ( 0.77 ) ^ { t }$ . Find the value of the computer after 6 years.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = ( x + 5 ) ^ { 2 }$

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

Finding Measures of Central Tendency for Prices and Heights

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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)=x+33f ( x ) = \sqrt [ 3 ] { x + 3 }f(x)=3x+3​

Graph the relation using solid circles and the inverse using open circles. - {(−9,3),(9,−3),(−7,−1),(7,1)}\{ ( - 9,3 ) , ( 9 , - 3 ) , ( - 7 , - 1 ) , ( 7,1 ) \}{(−9,3),(9,−3),(−7,−1),(7,1)}

Graph. - x=2yx = 2 yx=2y

Find an equation of the inverse of the relation. - y=4+6xy = 4 + 6 xy=4+6x

Find f(x)and g(x)such that h(x)= (f ° g)(x). - h(x)=8x2+7h ( x ) = \frac { 8 } { x ^ { 2 } } + 7h(x)=x28​+7

Determine whether the function is one-to-one. - f(x)=∣36−x2∣f ( x ) = \left| 36 - x ^ { 2 } \right|f(x)=​36−x2​

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=(x+5)2f ( x ) = ( x + 5 ) ^ { 2 }f(x)=(x+5)2