Question 1

For the given function f(x), find f-1(x).
-f(x) = 8x

Accepted Answer

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

Question 2

Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = \frac { 4 } { x ^ { 6 } }$ and $g ( x ) = 2 - x$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0,2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  $( - \infty , 0 ) \cup ( 0,2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 3

Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = x ^ { 2 } + 4 x + 10$$

Accepted Answer

A)  No $x$-intercepts, $( 0,10 )$ 
B)  No x-intercepts, $( 0 , - 10 )$ 
C)  $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0 , - 10 )$ 
D)  $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0,10 )$ 
A)  No $x$-intercepts, $( 0,10 )$ 
B)  No x-intercepts, $( 0 , - 10 )$ 
C)  $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0 , - 10 )$ 
D)  $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0,10 )$

Question 4

Solve the problem.
-If an object is thrown upward with an initial velocity of $14 \mathrm { ft }$ per sec, then its height (in feet) is given by $h ( t ) = - 14 t ^ { 2 } + 56 t$ after time $t$ seconds. What is its maximum height?

Accepted Answer

A)  $198 \mathrm { ft }$ 
B)  $56 \mathrm { ft }$ 
C)  $28 \mathrm { ft }$ 
D)  $196 \mathrm { ft }$ 
A)  $198 \mathrm { ft }$ 
B)  $56 \mathrm { ft }$ 
C)  $28 \mathrm { ft }$ 
D)  $196 \mathrm { ft }$

Question 5

For the given function f(x), find f-1(x).
-$$f ( x ) = - \frac { 2 } { x }$$

Accepted Answer

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

Question 6

Given f(x) and g(x), find the indicated composition and evaluate.
-$$f ( x ) = x ^ { 2 } + 3 ; g ( x ) = 4 x + 5$$
Find $( g \circ f ) ( 7 )$.

Accepted Answer

A)  203 
B)  57 
C)  1092 
D)  213 
A)  203 
B)  57 
C)  1092 
D)  213

Question 7

For the given functions f(x) and g(x), find (f ∙ g)(x) or $ \left(\frac{f}{g}\right)(x) $ as indicated.
-$$f ( x ) = 8 x - 9 , g ( x ) = 6 x - 6$$
Find $( f \cdot g ) ( x )$.

Accepted Answer

A)  $48 x ^ { 2 } - 102 x + 54$ 
B)  $14 x ^ { 2 } - 102 x - 15$ 
C)  $48 x ^ { 2 } - 60 x + 54$ 
D)  $48 x ^ { 2 } + 54$ 
A)  $48 x ^ { 2 } - 102 x + 54$ 
B)  $14 x ^ { 2 } - 102 x - 15$ 
C)  $48 x ^ { 2 } - 60 x + 54$ 
D)  $48 x ^ { 2 } + 54$

For the given function f(x), find f-1(x). -f(x) = 8x

Given f(x) and g(x), find the indicated composition and state its domain. -For $f ( x ) = \frac { 4 } { x ^ { 6 } }$ and $g ( x ) = 2 - x$ , what is the domain of $f \circ g$ ?

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = x ^ { 2 } + 4 x + 10$

Solve the problem. -If an object is thrown upward with an initial velocity of $14 \mathrm { ft }$ per sec, then its height (in feet) is given by $h ( t ) = - 14 t ^ { 2 } + 56 t$ after time $t$ seconds. What is its maximum height?

For the given function f(x), find f-1(x). - $f ( x ) = - \frac { 2 } { x }$

Given f(x) and g(x), find the indicated composition and evaluate. - $f ( x ) = x ^ { 2 } + 3 ; g ( x ) = 4 x + 5$ Find $( g \circ f ) ( 7 )$ .

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = 8 x - 9 , g ( x ) = 6 x - 6$ Find $( f \cdot g ) ( x )$ .

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 11: Functions