Question 1

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=\frac{9}{x} ; g(x)=5 x^{2}$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$.

Accepted Answer

A)  $\frac{9}{5 x^{2}}$, all real numbers except 0 
B)  $\frac{5 x^{2}}{9}$, all real numbers 
C)  $\frac{405}{x^{2}}$, all real numbers except 0 
D)  $\frac{5 x^{2}}{81}$, all real numbers 
A)  $\frac{9}{5 x^{2}}$, all real numbers except 0 
B)  $\frac{5 x^{2}}{9}$, all real numbers 
C)  $\frac{405}{x^{2}}$, all real numbers except 0 
D)  $\frac{5 x^{2}}{81}$, all real numbers

Question 2

Solve.
-$\log _{7} \mathrm{x}=2$

Accepted Answer

A)  $\{1000\}$ 
B)  $\{49\}$ 
C)  $\{-128\}$ 
D)  $\{14\}$ 
A)  $\{1000\}$ 
B)  $\{49\}$ 
C)  $\{-128\}$ 
D)  $\{14\}$

Question 3

Determine whether function is one-to-one.
-$\{(-7,3),(-6,3),(-5,-5),(-4,1)\}$

Accepted Answer

A) True 
 B)False

Question 4

Solve. Round to the nearest thousandth, if necessary
-$13^{ \mathrm{x}-1}=23$

Accepted Answer

A)  $\{2.222\}$ 
B)  $\{2.769\}$ 
C)  $\{1.818\}$ 
D)  $\{2.018\}$ 
A)  $\{2.222\}$ 
B)  $\{2.769\}$ 
C)  $\{1.818\}$ 
D)  $\{2.018\}$

Question 5

Evaluate the given function
-$f(x)=\left(\frac{1}{3}\right)^{x}, f(2)$

Accepted Answer

A)  $\frac{1}{9}$ 
B)  9 
C)  $\frac{1}{8}$ 
D)  $\frac{1}{6}$ 
A)  $\frac{1}{9}$ 
B)  9 
C)  $\frac{1}{8}$ 
D)  $\frac{1}{6}$

Question 6

Solve.
-$\log _{4}(6 \mathrm{x}-7)=\log _{4}(4 \mathrm{x}+2)$

Accepted Answer

A)  $\left\{\frac{9}{2}\right\}$ 
B)  $\{-5\}$ 
C)  $\left\{-\frac{5}{2}\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{9}{2}\right\}$ 
B)  $\{-5\}$ 
C)  $\left\{-\frac{5}{2}\right\}$ 
D)  $\varnothing$

Question 7

Solve the problem.
-Find $(f \cdot g)(2)$ when $f(x)=x-6$ and $g(x)=-3 x^{2}+12 x-4$.

Accepted Answer

A)  -96 
B)  -32 
C)  64 
D)  -128 
A)  -96 
B)  -32 
C)  64 
D)  -128

Question 8

Evaluate the given function. Round to the nearest thousandth.
-$f(x)=e^{x}, f(-2)$

Accepted Answer

A)  0.135 
B)  -5.437 
C)  0.693 
D)  0.150 
A)  0.135 
B)  -5.437 
C)  0.693 
D)  0.150

Question 9

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=\sqrt{2 x+11}, g(x)=x-12$
Find (f $\circ g)(x)$ and state its domain.

Accepted Answer

A)  $\sqrt{2 x-13}$, all real numbers except $\frac{13}{2}$ 
B)  $\sqrt{2 x+13},\left[-\frac{13}{2}, \infty\right)$ 
C)  $\sqrt{2 x-13},\left[\frac{13}{2}, \infty\right)$ 
D)  $\sqrt{2 x+13}$, all real numbers exœet $-\frac{13}{2}$ 
A)  $\sqrt{2 x-13}$, all real numbers except $\frac{13}{2}$ 
B)  $\sqrt{2 x+13},\left[-\frac{13}{2}, \infty\right)$ 
C)  $\sqrt{2 x-13},\left[\frac{13}{2}, \infty\right)$ 
D)  $\sqrt{2 x+13}$, all real numbers exœet $-\frac{13}{2}$

Question 10

For the given graph of a one-to-one function f(x), graph its inverse functionf-1(x) using a dashed line
-

Accepted Answer

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

Question 11

Solve.
-$2^{9-3 x}=1$

Accepted Answer

A)  $\{-3\}$ 
B)  $\{9\}$ 
C)  $\{3\}$. 
D)  $\left\{\frac{1}{3}\right\}$ 
A)  $\{-3\}$ 
B)  $\{9\}$ 
C)  $\{3\}$. 
D)  $\left\{\frac{1}{3}\right\}$

Question 12

Rewrite in logarithmic form
-$3^{2}=9$

Accepted Answer

A)  $\log _{2} 9=3$ 
B)  $\log _{3} 9=2$ 
C)  $\log _{9} 3=2$ 
D)  $\log _{3} 2=9$ 
A)  $\log _{2} 9=3$ 
B)  $\log _{3} 9=2$ 
C)  $\log _{9} 3=2$ 
D)  $\log _{3} 2=9$

Question 13

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=-7 x$

Accepted Answer

A)  $f^{-1}(x)=7+x$ 
B)  $f^{-1}(x)=-\frac{x}{7}$ 
C)  $\mathrm{f}^{-1}(\mathrm{x})=7 \mathrm{x}$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=-\frac{7}{\mathrm{x}}$ 
A)  $f^{-1}(x)=7+x$ 
B)  $f^{-1}(x)=-\frac{x}{7}$ 
C)  $\mathrm{f}^{-1}(\mathrm{x})=7 \mathrm{x}$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=-\frac{7}{\mathrm{x}}$

Question 14

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers.
-$\log _{b} y-\log _{b} b$

Accepted Answer

A)  $\log _{b} \frac{b}{y}$ 
B)  $\log _{2 b} \frac{y}{b}$ 
C)  $\log _{\mathrm{b}} \mathrm{y}-\mathrm{b}$ 
D)  $\log _{b} \frac{y}{b}$ 
A)  $\log _{b} \frac{b}{y}$ 
B)  $\log _{2 b} \frac{y}{b}$ 
C)  $\log _{\mathrm{b}} \mathrm{y}-\mathrm{b}$ 
D)  $\log _{b} \frac{y}{b}$

Question 15

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers.
-$\log _{5} 7+\log _{5} 11$

Accepted Answer

A)  $\log _{10} 18$ 
B)  $\log _{5} 18$ 
C)  $\log _{10} 77$ 
D)  $\log _{5} 77$ 
A)  $\log _{10} 18$ 
B)  $\log _{5} 18$ 
C)  $\log _{10} 77$ 
D)  $\log _{5} 77$

Question 16

Solve the problem.
-A certain country's population $\mathrm{P}(\mathrm{t})$, in millions, tyears after 1990 can be approximated by $P(t)=3.495(1.016)^{t}$.
In what year did the country's population reach 4 million?

Accepted Answer

A)  About 1999 
B)  About 2004 
C)  About 2009 
D)  About 1989 
A)  About 1999 
B)  About 2004 
C)  About 2009 
D)  About 1989

Question 17

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b} 27$

Accepted Answer

A)  $3 \mathrm{~B}$ 
B)  $2 \mathrm{C}$ 
C)  $2 B$ 
D)  $3 \mathrm{C}$ 
A)  $3 \mathrm{~B}$ 
B)  $2 \mathrm{C}$ 
C)  $2 B$ 
D)  $3 \mathrm{C}$

Question 18

For the given function $f(x)$, find its inverse.
-$f(x)=e^{x+8}$

Accepted Answer

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

Question 19

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers.
-$\log _{x}(8 y z)$

Accepted Answer

A)  $\log _{x} 8+\log _{x} y+\log _{x} z$ 
B)  $\log _{x}(8+y+z)$ 
C)  $\log 8 y+\log 8 z$ 
D)  $\left(\log _{x} 8\right)\left(\log _{x} y\right)\left(\log _{x} z\right)$ 
A)  $\log _{x} 8+\log _{x} y+\log _{x} z$ 
B)  $\log _{x}(8+y+z)$ 
C)  $\log 8 y+\log 8 z$ 
D)  $\left(\log _{x} 8\right)\left(\log _{x} y\right)\left(\log _{x} z\right)$

Question 20

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _{7} 36.52$

Accepted Answer

A)  0.5409 
B)  1.5625 
C)  1.8489 
D)  5.2171 
A)  0.5409 
B)  1.5625 
C)  1.8489 
D)  5.2171

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=\frac{9}{x} ; g(x)=5 x^{2}$ Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

Solve. - $\log _{7} \mathrm{x}=2$

Determine whether function is one-to-one. - $\{(-7,3),(-6,3),(-5,-5),(-4,1)\}$

Solve. Round to the nearest thousandth, if necessary - $13^{ \mathrm{x}-1}=23$

Evaluate the given function - $f(x)=\left(\frac{1}{3}\right)^{x}, f(2)$

Solve. - $\log _{4}(6 \mathrm{x}-7)=\log _{4}(4 \mathrm{x}+2)$

Solve the problem. -Find $(f \cdot g)(2)$ when $f(x)=x-6$ and $g(x)=-3 x^{2}+12 x-4$ .

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{x}, f(-2)$

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=\sqrt{2 x+11}, g(x)=x-12$ Find (f $\circ g)(x)$ and state its domain.

For the given graph of a one-to-one function f(x), graph its inverse functionf-1(x) using a dashed line -

Solve. - $2^{9-3 x}=1$

Rewrite in logarithmic form - $3^{2}=9$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=-7 x$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{b} y-\log _{b} b$

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{5} 7+\log _{5} 11$

Solve the problem. -A certain country's population $\mathrm{P}(\mathrm{t})$ , in millions, tyears after 1990 can be approximated by $P(t)=3.495(1.016)^{t}$ . In what year did the country's population reach 4 million?

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b} 27$

For the given function $f(x)$ , find its inverse. - $f(x)=e^{x+8}$

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{x}(8 y z)$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _{7} 36.52$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Logarithmic and Exponential Functions

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=9x;g(x)=5x2f(x)=\frac{9}{x} ; g(x)=5 x^{2}f(x)=x9​;g(x)=5x2 Find (g∘f)(x)(\mathrm{g} \circ \mathrm{f})(\mathrm{x})(g∘f)(x) .

Solve. - log⁡7x=2\log _{7} \mathrm{x}=2log7​x=2

Determine whether function is one-to-one. - {(−7,3),(−6,3),(−5,−5),(−4,1)}\{(-7,3),(-6,3),(-5,-5),(-4,1)\}{(−7,3),(−6,3),(−5,−5),(−4,1)}

Solve. Round to the nearest thousandth, if necessary - 13x−1=2313^{ \mathrm{x}-1}=2313x−1=23

Evaluate the given function - f(x)=(13)x,f(2)f(x)=\left(\frac{1}{3}\right)^{x}, f(2)f(x)=(31​)x,f(2)

Solve. - log⁡4(6x−7)=log⁡4(4x+2)\log _{4}(6 \mathrm{x}-7)=\log _{4}(4 \mathrm{x}+2)log4​(6x−7)=log4​(4x+2)

Solve the problem. -Find (f⋅g)(2)(f \cdot g)(2)(f⋅g)(2) when f(x)=x−6f(x)=x-6f(x)=x−6 and g(x)=−3x2+12x−4g(x)=-3 x^{2}+12 x-4g(x)=−3x2+12x−4 .

Evaluate the given function. Round to the nearest thousandth. - f(x)=ex,f(−2)f(x)=e^{x}, f(-2)f(x)=ex,f(−2)

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=2x+11,g(x)=x−12f(x)=\sqrt{2 x+11}, g(x)=x-12f(x)=2x+11​,g(x)=x−12 Find (f ∘g)(x)\circ g)(x)∘g)(x) and state its domain.