Question 1

Find the exact value of $6 \log _ { 2 } 6 - 3 \log _ { 2 } 9$

Accepted Answer

The answer of Find the exact value of \(6 \log...

Question 2

Given $f ( x ) = 2 x + 1$ and $h ( x ) = 2 x ^ { 2 } + 4 x + 1$ , find a function $g$ such that $f ( g ( x ) ) = h ( x )$

Accepted Answer

A)  $g ( x ) = \left( x ^ { 2 } + 1 \right) ^ { 2 }$ 
B)  $g ( x ) = x ^ { 2 } + 2$ 
C)  $g ( x ) = x ^ { 2 } + 4 x$ 
D)  $g ( x ) = x ^ { 2 } + 2 x$ 
A)  $g ( x ) = \left( x ^ { 2 } + 1 \right) ^ { 2 }$ 
B)  $g ( x ) = x ^ { 2 } + 2$ 
C)  $g ( x ) = x ^ { 2 } + 4 x$ 
D)  $g ( x ) = x ^ { 2 } + 2 x$

Question 3

If $f ( x ) = \sqrt { 2 x - 1 }$ , find $\frac { f ( 1 + h ) - f ( 1 ) } { h }$

Accepted Answer

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

Question 4

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x ) - 3$

Accepted Answer

A)  (0, 7) 
B)  (3, 4) 
C)  (3, 7) 
D)  (0, 4) 
A)  (0, 7) 
B)  (3, 4) 
C)  (3, 7) 
D)  (0, 4)

Question 5

Find the domain and range of $f ( x ) = \sqrt { 2 - x } + 1$

Accepted Answer

The answer of Find the domain and range of \(f...

Question 6

Given $f ( x ) = x ^ { 2 } + 1$ and $g ( x ) = 3 x + 2$ , find all values of $X$ such that $f ( g ( x ) ) = g ( f ( x ) )$

Accepted Answer

A)  2, 3 
B)  0, 2 
C)  0, - 2 
D)  0, 3 
A)  2, 3 
B)  0, 2 
C)  0, - 2 
D)  0, 3

Question 7

Write $f ( x ) = | 3 - 2 x |$ as a piecewise function.

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 2 x & x \leq 3 / 2 \
3 - 2 x & x > 3 / 2
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 - 2 x & x \leq 3 / 2 \
3 + 2 x & x > 3 / 2
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 2 x & x  3 / 2 \
3 - 2 x & x \leq 3 / 2
\end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 2 x & x \leq 3 / 2 \
3 - 2 x & x > 3 / 2
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 - 2 x & x \leq 3 / 2 \
3 + 2 x & x > 3 / 2
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 2 x & x  3 / 2 \
3 - 2 x & x \leq 3 / 2
\end{array} \right.$

Question 8

Given that $f ( x ) = \frac { 1 } { x } + 1$ and $g ( x ) = \frac { 1 } { 1 + x }$ , find $( f \circ g ) ( 2 )$ , and their domains.

Accepted Answer

The answer of Given that \(f ( x ) =...

Question 9

Solve the following equation for x, on the interval $[ 0 , \pi ]$ : $2 \sin 2 x = 1$

Accepted Answer

The answer of Solve the following equation for x, on...

Question 10

Express the following as a polynomial function of $X :$ $5 \exp ( \ln 3 ) + 2 \ln \left( e ^ { 3 x } \left( e ^ { x } \right) ^ { 2 } \right)$

Accepted Answer

The answer of Express the following as a polynomial function...

Question 11

Find the equation of a linear function whose graph has slope -2 and passes through the point (-1, 2). Write your answer in slope-intercept form.

Accepted Answer

A)  $y = - 2 x - 5$ 
B)  $y = - 2 x + 3$ 
C)  $y = - 2 x + 4$ 
D)  $y = - 2 x$ 
A)  $y = - 2 x - 5$ 
B)  $y = - 2 x + 3$ 
C)  $y = - 2 x + 4$ 
D)  $y = - 2 x$

Question 12

Express $f ( x ) = \sqrt [ 3 ] { 1 + \sqrt { x } }$ as a composition of three functions: $g$ and $h$ such that $f = g \circ h$

Accepted Answer

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

Question 13

Solve the following equation for $X$ : $5 e ^ { - 2 x } = 6$

Accepted Answer

The answer of Solve the following equation for $X$ :...

Question 14

Find the domain and range of $f ( x ) = \frac { 1 } { \sqrt { x - 3 } }$

Accepted Answer

A)  Domain: $( - \infty , 3 ]$ Range: $[ 0 , \infty )$ 
B)  Domain: $[ 0 , \infty )$ Range: $( - \infty , 3 ]$ 
C)  Domain: $( - \infty , 3 )$ Range: $( 0 , \infty )$ 
D)  Domain: $( 3 , \infty )$ Range: $( 0 , \infty )$ 
A)  Domain: $( - \infty , 3 ]$ Range: $[ 0 , \infty )$ 
B)  Domain: $[ 0 , \infty )$ Range: $( - \infty , 3 ]$ 
C)  Domain: $( - \infty , 3 )$ Range: $( 0 , \infty )$ 
D)  Domain: $( 3 , \infty )$ Range: $( 0 , \infty )$

Question 15

Which of the following expressions is/are defined?
A. $\sin ^ { - 1 } \left( - \frac { 1 } { 5 } \right)$
B. $\sin ^ { - 1 } \left( \frac { 3 } { 2 } \right)$
C. $\tan ^ { - 1 } ( 2 )$

Accepted Answer

A)  A and B 
B)  B and C 
C)  A and C 
D)  Only A 
A)  A and B 
B)  B and C 
C)  A and C 
D)  Only A

Question 16

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\sin \left( \cos ^ { - 1 } 3 x \right)$

Accepted Answer

A)  $\sqrt { 1 - x ^ { 2 } }$ 
B)  $\sqrt { x ^ { 2 } - 1 }$ 
C)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
D)  $\sqrt { 1 - 3 x ^ { 2 } }$ 
A)  $\sqrt { 1 - x ^ { 2 } }$ 
B)  $\sqrt { x ^ { 2 } - 1 }$ 
C)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
D)  $\sqrt { 1 - 3 x ^ { 2 } }$

Question 17

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( g \circ f ) ( x )$ 
 $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
\hline f ( x ) & 0 & 1 & 3 & 2 & 3 & 0 & 2 \
\hline g ( x ) & 1 & 0 & 1 & 1 & 0 & 1 & 0 \
\hline
\end{array}$$

Accepted Answer

\[\begin{array} { | l | l | l

Question 18

Find the domain and range of $f ( x ) = 2 + e ^ { x - 1 }$

Accepted Answer

The answer of Find the domain and range of \(f...

Question 19

Describe the function $f ( t ) = - 5 t + 1$ as a set of ordered pairs.

Accepted Answer

The answer of Describe the function \(f ( t )...

Question 20

$f ( x ) = \left\{ \begin{array} { r r } 
x ^ { 2 } + 3 & x < 0 \
3 - x & x \geq 0
\end{array} \right.$ Calculate $f ( - 1 ) , f ( 0 )$ and $f ( 2 )$

Accepted Answer

The answer of \(f ( x ) = \left\{ \begin{array}...

Find the exact value of $6 \log _ { 2 } 6 - 3 \log _ { 2 } 9$

Given $f ( x ) = 2 x + 1$ and $h ( x ) = 2 x ^ { 2 } + 4 x + 1$ , find a function $g$ such that $f ( g ( x ) ) = h ( x )$

If $f ( x ) = \sqrt { 2 x - 1 }$ , find $\frac { f ( 1 + h ) - f ( 1 ) } { h }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x ) - 3$

Find the domain and range of $f ( x ) = \sqrt { 2 - x } + 1$

Given $f ( x ) = x ^ { 2 } + 1$ and $g ( x ) = 3 x + 2$ , find all values of $X$ such that $f ( g ( x ) ) = g ( f ( x ) )$

Write $f ( x ) = | 3 - 2 x |$ as a piecewise function.

Given that $f ( x ) = \frac { 1 } { x } + 1$ and $g ( x ) = \frac { 1 } { 1 + x }$ , find $( f \circ g ) ( 2 )$ , and their domains.

Solve the following equation for x, on the interval $[ 0 , \pi ]$ : $2 \sin 2 x = 1$

Express the following as a polynomial function of $X :$ $5 \exp ( \ln 3 ) + 2 \ln \left( e ^ { 3 x } \left( e ^ { x } \right) ^ { 2 } \right)$

Find the equation of a linear function whose graph has slope -2 and passes through the point (-1, 2). Write your answer in slope-intercept form.

Express $f ( x ) = \sqrt [ 3 ] { 1 + \sqrt { x } }$ as a composition of three functions: $g$ and $h$ such that $f = g \circ h$

Solve the following equation for $X$ : $5 e ^ { - 2 x } = 6$

Find the domain and range of $f ( x ) = \frac { 1 } { \sqrt { x - 3 } }$

Which of the following expressions is/are defined? A. $\sin ^ { - 1 } \left( - \frac { 1 } { 5 } \right)$ B. $\sin ^ { - 1 } \left( \frac { 3 } { 2 } \right)$ C. $\tan ^ { - 1 } ( 2 )$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\sin \left( \cos ^ { - 1 } 3 x \right)$

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( g \circ f ) ( x )$ x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Find the domain and range of $f ( x ) = 2 + e ^ { x - 1 }$

Describe the function $f ( t ) = - 5 t + 1$ as a set of ordered pairs.

$f ( x ) = \left\{ \begin{array} { r r } x ^ { 2 } + 3 & x < 0 \\3 - x & x \geq 0\end{array} \right.$ Calculate $f ( - 1 ) , f ( 0 )$ and $f ( 2 )$

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Filters

Exam 15: Functions and Precalculus

Find the exact value of 6log⁡26−3log⁡296 \log _ { 2 } 6 - 3 \log _ { 2 } 96log2​6−3log2​9

Given f(x)=2x+1f ( x ) = 2 x + 1f(x)=2x+1 and h(x)=2x2+4x+1h ( x ) = 2 x ^ { 2 } + 4 x + 1h(x)=2x2+4x+1 , find a function ggg such that f(g(x))=h(x)f ( g ( x ) ) = h ( x )f(g(x))=h(x)

If f(x)=2x−1f ( x ) = \sqrt { 2 x - 1 }f(x)=2x−1​ , find f(1+h)−f(1)h\frac { f ( 1 + h ) - f ( 1 ) } { h }hf(1+h)−f(1)​

Suppose (3, 7) is a point on the graph of f(x)f ( x )f(x) , find a point on the graph of f(x)−3f ( x ) - 3f(x)−3

Find the domain and range of f(x)=2−x+1f ( x ) = \sqrt { 2 - x } + 1f(x)=2−x​+1

Given f(x)=x2+1f ( x ) = x ^ { 2 } + 1f(x)=x2+1 and g(x)=3x+2g ( x ) = 3 x + 2g(x)=3x+2 , find all values of XXX such that f(g(x))=g(f(x))f ( g ( x ) ) = g ( f ( x ) )f(g(x))=g(f(x))

Write f(x)=∣3−2x∣f ( x ) = | 3 - 2 x |f(x)=∣3−2x∣ as a piecewise function.

Given that f(x)=1x+1f ( x ) = \frac { 1 } { x } + 1f(x)=x1​+1 and g(x)=11+xg ( x ) = \frac { 1 } { 1 + x }g(x)=1+x1​ , find (f∘g)(2)( f \circ g ) ( 2 )(f∘g)(2) , and their domains.

Solve the following equation for x, on the interval [0,π][ 0 , \pi ][0,π] : 2sin⁡2x=12 \sin 2 x = 12sin2x=1

Express the following as a polynomial function of X:X :X: 5exp⁡(ln⁡3)+2ln⁡(e3x(ex)2)5 \exp ( \ln 3 ) + 2 \ln \left( e ^ { 3 x } \left( e ^ { x } \right) ^ { 2 } \right)5exp(ln3)+2ln(e3x(ex)2)

Find the equation of a linear function whose graph has slope -2 and passes through the point (-1, 2). Write your answer in slope-intercept form.

Express f(x)=1+x3f ( x ) = \sqrt [ 3 ] { 1 + \sqrt { x } }f(x)=31+x​​ as a composition of three functions: ggg and hhh such that f=g∘hf = g \circ hf=g∘h

Solve the following equation for XXX : 5e−2x=65 e ^ { - 2 x } = 65e−2x=6

Find the domain and range of f(x)=1x−3f ( x ) = \frac { 1 } { \sqrt { x - 3 } }f(x)=x−3​1​

Which of the following expressions is/are defined? A. sin⁡−1(−15)\sin ^ { - 1 } \left( - \frac { 1 } { 5 } \right)sin−1(−51​) B. sin⁡−1(32)\sin ^ { - 1 } \left( \frac { 3 } { 2 } \right)sin−1(23​) C. tan⁡−1(2)\tan ^ { - 1 } ( 2 )tan−1(2)

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions sin⁡(cos⁡−13x)\sin \left( \cos ^ { - 1 } 3 x \right)sin(cos−13x)

Table below defines two functions fff and ggg Create an additional row for the table for the function (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Find the domain and range of f(x)=2+ex−1f ( x ) = 2 + e ^ { x - 1 }f(x)=2+ex−1

Describe the function f(t)=−5t+1f ( t ) = - 5 t + 1f(t)=−5t+1 as a set of ordered pairs.

f(x)={x2+3x<03−xx≥0f ( x ) = \left\{ \begin{array} { r r } x ^ { 2 } + 3 & x < 0 \\3 - x & x \geq 0\end{array} \right.f(x)={x2+33−x​x<0x≥0​ Calculate f(−1),f(0)f ( - 1 ) , f ( 0 )f(−1),f(0) and f(2)f ( 2 )f(2)

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Filters

Find the exact value of $6 \log _ { 2 } 6 - 3 \log _ { 2 } 9$

Given $f ( x ) = 2 x + 1$ and $h ( x ) = 2 x ^ { 2 } + 4 x + 1$ , find a function $g$ such that $f ( g ( x ) ) = h ( x )$

If $f ( x ) = \sqrt { 2 x - 1 }$ , find $\frac { f ( 1 + h ) - f ( 1 ) } { h }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x ) - 3$

Find the domain and range of $f ( x ) = \sqrt { 2 - x } + 1$

Given $f ( x ) = x ^ { 2 } + 1$ and $g ( x ) = 3 x + 2$ , find all values of $X$ such that $f ( g ( x ) ) = g ( f ( x ) )$

Write $f ( x ) = | 3 - 2 x |$ as a piecewise function.

Given that $f ( x ) = \frac { 1 } { x } + 1$ and $g ( x ) = \frac { 1 } { 1 + x }$ , find $( f \circ g ) ( 2 )$ , and their domains.

Solve the following equation for x, on the interval $[ 0 , \pi ]$ : $2 \sin 2 x = 1$

Express the following as a polynomial function of $X :$ $5 \exp ( \ln 3 ) + 2 \ln \left( e ^ { 3 x } \left( e ^ { x } \right) ^ { 2 } \right)$

Express $f ( x ) = \sqrt [ 3 ] { 1 + \sqrt { x } }$ as a composition of three functions: $g$ and $h$ such that $f = g \circ h$

Solve the following equation for $X$ : $5 e ^ { - 2 x } = 6$

Find the domain and range of $f ( x ) = \frac { 1 } { \sqrt { x - 3 } }$

Which of the following expressions is/are defined? A. $\sin ^ { - 1 } \left( - \frac { 1 } { 5 } \right)$ B. $\sin ^ { - 1 } \left( \frac { 3 } { 2 } \right)$ C. $\tan ^ { - 1 } ( 2 )$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\sin \left( \cos ^ { - 1 } 3 x \right)$

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( g \circ f ) ( x )$ x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Find the domain and range of $f ( x ) = 2 + e ^ { x - 1 }$

Describe the function $f ( t ) = - 5 t + 1$ as a set of ordered pairs.

$f ( x ) = \left\{ \begin{array} { r r } x ^ { 2 } + 3 & x < 0 \\3 - x & x \geq 0\end{array} \right.$ Calculate $f ( - 1 ) , f ( 0 )$ and $f ( 2 )$