Question 1

Let $m(x)=e^{x}$ and $n(x)=\frac{x^{4}}{x+5}$. Does $m(n(x))=\frac{e^{4 x}}{e^{x}+5}$ ?

Accepted Answer

A) True 
 B)False

Question 2

Let $g(x)=\frac{6}{x}+6$. Does $g^{-1}(x)=\frac{6}{x-6}$ ?

Accepted Answer

A) True 
 B)False

Question 3

The function $h(x)$ is shown in the first figure.
 
Which transformation of $h(x)$ is shown in the second figure?

Accepted Answer

A)  $y=1 /h(x)$ 
B)  $y=-h(x)$ 
C)  $y=|h(x)|$ 
D)  $y=h(-x)$ 
A)  $y=1 /h(x)$ 
B)  $y=-h(x)$ 
C)  $y=|h(x)|$ 
D)  $y=h(-x)$

Question 4

Given the graph of $g$ below, which of the following is a solution to the equation $g(x)=1$ ?

Accepted Answer

A)  1 
B)  0 
C)  -3 
D)  3 
E)  2 
A)  1 
B)  0 
C)  -3 
D)  3 
E)  2

Question 5

Let $m(x)=f(g(x))$ and $n(x)=g(f(x))$. Using the table below gives $m(7)=$ -----------and $n(7)=$-----------------

Accepted Answer

The answer of Let $m(x)=f(g(x))$ and $n(x)=g(f(x))$. Using the table...

Question 6

Find the function $p(x)=f(x)-g(x)$ when $f(x)=4 x^{3}+7$ and $g(x)=2 x+9$.

Accepted Answer

The answer of Find the function $p(x)=f(x)-g(x)$ when $f(x)=4 x^{3}+7$...

Question 7

Let $v(x)=4 e^{x}+3 x$ and $u(x)=-2 x$. Find a simplified formula for the function $w(x)=(u(v(x)))^{2}$.

Accepted Answer

The answer of Let $v(x)=4 e^{x}+3 x$ and $u(x)=-2 x$....

Question 8

Let $f(x)=x^{2}+1$ and $h(x)=\sqrt{x-3}$. Does $h(f(x))=\sqrt{x^{2}-3}$ ?

Accepted Answer

A) True 
 B)False

Question 9

Let $f(x)=x+3$ and $g(x)=x^{2}$. What is $4 f(x)-g(x)$ ?

Accepted Answer

A)  $-x^{2}+4 x+4$ 
B)  $-x^{2}+4 x+12$ 
C)  $-4 x^{2}+4 x+12$ 
D)  $-4 x^{2}+4 x+4$ 
A)  $-x^{2}+4 x+4$ 
B)  $-x^{2}+4 x+12$ 
C)  $-4 x^{2}+4 x+12$ 
D)  $-4 x^{2}+4 x+4$

Let $m(x)=e^{x}$ and $n(x)=\frac{x^{4}}{x+5}$ . Does $m(n(x))=\frac{e^{4 x}}{e^{x}+5}$ ?

Let $g(x)=\frac{6}{x}+6$ . Does $g^{-1}(x)=\frac{6}{x-6}$ ?

The function $h(x)$ is shown in the first figure. Which transformation of $h(x)$ is shown in the second figure?

Given the graph of $g$ below, which of the following is a solution to the equation $g(x)=1$ ?

Let $m(x)=f(g(x))$ and $n(x)=g(f(x))$ . Using the table below gives $m(7)=$ -----------and $n(7)=$ -----------------

Find the function $p(x)=f(x)-g(x)$ when $f(x)=4 x^{3}+7$ and $g(x)=2 x+9$ .

Let $v(x)=4 e^{x}+3 x$ and $u(x)=-2 x$ . Find a simplified formula for the function $w(x)=(u(v(x)))^{2}$ .

Let $f(x)=x^{2}+1$ and $h(x)=\sqrt{x-3}$ . Does $h(f(x))=\sqrt{x^{2}-3}$ ?

Let $f(x)=x+3$ and $g(x)=x^{2}$ . What is $4 f(x)-g(x)$ ?

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

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Exam 10: Compositions, Inverses, and Combinations of Functions

Let m(x)=exm(x)=e^{x}m(x)=ex and n(x)=x4x+5n(x)=\frac{x^{4}}{x+5}n(x)=x+5x4​ . Does m(n(x))=e4xex+5m(n(x))=\frac{e^{4 x}}{e^{x}+5}m(n(x))=ex+5e4x​ ?

Let g(x)=6x+6g(x)=\frac{6}{x}+6g(x)=x6​+6 . Does g−1(x)=6x−6g^{-1}(x)=\frac{6}{x-6}g−1(x)=x−66​ ?

The function h(x)h(x)h(x) is shown in the first figure. Which transformation of h(x)h(x)h(x) is shown in the second figure?

Given the graph of ggg below, which of the following is a solution to the equation g(x)=1g(x)=1g(x)=1 ?

Let m(x)=f(g(x))m(x)=f(g(x))m(x)=f(g(x)) and n(x)=g(f(x))n(x)=g(f(x))n(x)=g(f(x)) . Using the table below gives m(7)=m(7)=m(7)= -----------and n(7)=n(7)=n(7)= -----------------

Find the function p(x)=f(x)−g(x)p(x)=f(x)-g(x)p(x)=f(x)−g(x) when f(x)=4x3+7f(x)=4 x^{3}+7f(x)=4x3+7 and g(x)=2x+9g(x)=2 x+9g(x)=2x+9 .

Let v(x)=4ex+3xv(x)=4 e^{x}+3 xv(x)=4ex+3x and u(x)=−2xu(x)=-2 xu(x)=−2x . Find a simplified formula for the function w(x)=(u(v(x)))2w(x)=(u(v(x)))^{2}w(x)=(u(v(x)))2 .

Let f(x)=x2+1f(x)=x^{2}+1f(x)=x2+1 and h(x)=x−3h(x)=\sqrt{x-3}h(x)=x−3​ . Does h(f(x))=x2−3h(f(x))=\sqrt{x^{2}-3}h(f(x))=x2−3​ ?

Let f(x)=x+3f(x)=x+3f(x)=x+3 and g(x)=x2g(x)=x^{2}g(x)=x2 . What is 4f(x)−g(x)4 f(x)-g(x)4f(x)−g(x) ?

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

Let $m(x)=e^{x}$ and $n(x)=\frac{x^{4}}{x+5}$ . Does $m(n(x))=\frac{e^{4 x}}{e^{x}+5}$ ?

Let $g(x)=\frac{6}{x}+6$ . Does $g^{-1}(x)=\frac{6}{x-6}$ ?

The function $h(x)$ is shown in the first figure. Which transformation of $h(x)$ is shown in the second figure?

Given the graph of $g$ below, which of the following is a solution to the equation $g(x)=1$ ?

Let $m(x)=f(g(x))$ and $n(x)=g(f(x))$ . Using the table below gives $m(7)=$ -----------and $n(7)=$ -----------------

Find the function $p(x)=f(x)-g(x)$ when $f(x)=4 x^{3}+7$ and $g(x)=2 x+9$ .

Let $v(x)=4 e^{x}+3 x$ and $u(x)=-2 x$ . Find a simplified formula for the function $w(x)=(u(v(x)))^{2}$ .

Let $f(x)=x^{2}+1$ and $h(x)=\sqrt{x-3}$ . Does $h(f(x))=\sqrt{x^{2}-3}$ ?

Let $f(x)=x+3$ and $g(x)=x^{2}$ . What is $4 f(x)-g(x)$ ?