Question 1

Solve.
-$4^{12-2 x}=4096$

Accepted Answer

A)  $\{3\}$ 
B)  $\{6\}$ 
C)  $\{1024\}$ 
D)  $\{3\}$. 
A)  $\{3\}$ 
B)  $\{6\}$ 
C)  $\{1024\}$ 
D)  $\{3\}$.

Question 2

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=\frac{9 x-5}{2 x-7}$

Accepted Answer

A)  Not one- to- one 
B)  $f^{-1}(x)=\frac{2 x-9}{7 x-5}$ 
C)  $f^{-1}(x)=\frac{7 x-5}{2 x-9}$ 
D)  $f^{-1}(x)=\frac{9 x-5}{2 x-7}$ 
A)  Not one- to- one 
B)  $f^{-1}(x)=\frac{2 x-9}{7 x-5}$ 
C)  $f^{-1}(x)=\frac{7 x-5}{2 x-9}$ 
D)  $f^{-1}(x)=\frac{9 x-5}{2 x-7}$

Question 3

Solve.
-$\log _{2} 16=\mathrm{x}$

Accepted Answer

A)  $\{32\}$ 
B)  $\{4\}$ 
C)  $\{18\}$ 
D)  $\{8\}$ 
A)  $\{32\}$ 
B)  $\{4\}$ 
C)  $\{18\}$ 
D)  $\{8\}$

Question 4

Solve the problem.
-Find (f - g)(4) when $f(x)=3 x^{2}+5$ and $g(x)=x+1$.

Accepted Answer

A)  56 
B)  50 
C)  -57 
D)  48 
A)  56 
B)  50 
C)  -57 
D)  48

Question 5

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-5 x+8, g(x)=x^{2}-3 x-9$
Find $(f+g)(x)$.

Accepted Answer

A)  $x^{2}+3 x-1$ 
B)  $x^{2}-8 x-1$ 
C)  $x^{2}-8 x+12$ 
D)  $x^{2}+3 x+5$ 
A)  $x^{2}+3 x-1$ 
B)  $x^{2}-8 x-1$ 
C)  $x^{2}-8 x+12$ 
D)  $x^{2}+3 x+5$

Question 6

Solve.
-The population of a small country increases according to the function $B=1,300,000 e^{0.04 t}$, where $t$ is measured in years. How many people will the country have after 6 years?

Accepted Answer

A)  805,725 
B)  $1,652,624$ 
C)  $1,855,251$ 
D)  $2,259,141$ 
A)  805,725 
B)  $1,652,624$ 
C)  $1,855,251$ 
D)  $2,259,141$

Question 7

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-7 x+5, g(x)=-2 x+7$
Find $(f+g)(x)$.

Accepted Answer

A)  $-9 x+12$ 
B)  $-5 \mathrm{x}+12$ 
C)  $-2 \mathrm{x}+5$ 
D)  $3 \mathrm{x}$ 
A)  $-9 x+12$ 
B)  $-5 \mathrm{x}+12$ 
C)  $-2 \mathrm{x}+5$ 
D)  $3 \mathrm{x}$

Question 8

Solve.
-$4^{2 \mathrm{x}-18}=\frac{1}{16}$

Accepted Answer

A)  $\{-10\}$ 
B)  $\{8\}$ 
C)  $\{10\}$. 
D)  $\{8\}$. 
A)  $\{-10\}$ 
B)  $\{8\}$ 
C)  $\{10\}$. 
D)  $\{8\}$.

Question 9

Use the horizontal-line test to determine whether the function is one to one.
-

Accepted Answer

A) True 
 B)False

Question 10

Solve.
-$(\log 3 x)^{2}+2 \log 3 x-8=0$

Accepted Answer

A)  $\{9\}$ 
B)  $\left\{\frac{1}{81}\right\}$ 
C)  $\left\{\frac{1}{81}, 9\right\}$ 
D)  $\{4\}$ 
A)  $\{9\}$ 
B)  $\left\{\frac{1}{81}\right\}$ 
C)  $\left\{\frac{1}{81}, 9\right\}$ 
D)  $\{4\}$

Question 11

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$\log _{b} y^{3}$

Accepted Answer

A)  $b \log _{3} y$ 
B)  $\operatorname{blog}_{30} \mathrm{y}^{3}$ 
C)  $3 \log _{b} y$ 
D)  $3 \log _{b} y^{3}$ 
A)  $b \log _{3} y$ 
B)  $\operatorname{blog}_{30} \mathrm{y}^{3}$ 
C)  $3 \log _{b} y$ 
D)  $3 \log _{b} y^{3}$

Question 12

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _{8.3} 2.9$

Accepted Answer

A)  1.9876 
B)  0.4624 
C)  0.5031 
D)  0.3494 
A)  1.9876 
B)  0.4624 
C)  0.5031 
D)  0.3494

Question 13

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5$
Find $(f \cdot g)(x)$.

Accepted Answer

A)  $4 x^{4}-16 x^{3}+12 x^{2}-6 x+20$ 
B)  $4 x^{4}-16 x^{3}+16 x^{2}-6 x+20$ 
C)  $4 x^{4}-14 x^{3}+16 x^{2}-6 x+20$ 
D)  $4 x^{4}-14 x^{3}+12 x^{2}-6 x+20$ 
A)  $4 x^{4}-16 x^{3}+12 x^{2}-6 x+20$ 
B)  $4 x^{4}-16 x^{3}+16 x^{2}-6 x+20$ 
C)  $4 x^{4}-14 x^{3}+16 x^{2}-6 x+20$ 
D)  $4 x^{4}-14 x^{3}+12 x^{2}-6 x+20$

Question 14

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-8 x+8, g(x)=-5 x+9$
Find $(\mathrm{f}-\mathrm{g})(\mathrm{x})$.

Accepted Answer

A)  $3 \mathrm{x}$ 
B)  $-13 x-1$ 
C)  $-3 x-1$ 
D)  $-3 x+16$ 
A)  $3 \mathrm{x}$ 
B)  $-13 x-1$ 
C)  $-3 x-1$ 
D)  $-3 x+16$

Question 15

Solve the problem.
-Use the formula $L=10 \cdot \log \frac{I}{I_{0}}$, where the loudness of a sound in decibels is determined by $I$, the number of watts per square meter produced by the sound wave, and $\mathrm{I}_{0}=10^{-12}$ watts per square meter. What is the intensity of a noise measured at $93 \mathrm{db}$ ?

Accepted Answer

A)  $1.09 \times 10^{16}$ watts per square meter 
B)  $2 \times 10^{-2}$ watts per square meter 
C)  $9.3 \times 10^{-10}$ watts per square meter 
D)  $2 \times 10^{-3}$ watts per square meter 
A)  $1.09 \times 10^{16}$ watts per square meter 
B)  $2 \times 10^{-2}$ watts per square meter 
C)  $9.3 \times 10^{-10}$ watts per square meter 
D)  $2 \times 10^{-3}$ watts per square meter

Question 16

Evaluate the given function
-$\mathrm{f}(\mathrm{x})=4^{\mathrm{x}}, \mathrm{f}(4)$

Accepted Answer

A)  256 
B)  1 
C)  16 
D)  $\frac{1}{16}$ 
A)  256 
B)  1 
C)  16 
D)  $\frac{1}{16}$

Question 17

Solve.
-The number of acres in a landfill is given by the function $B=6500 e^{-0.04 t}$, where $t$ is measured in years. How many acres will the landfill have after 7 years? (Round to the nearest acre.)

Accepted Answer

A)  8274 acres 
B)  4913 acres 
C)  3411 acres 
D)  3593 acres 
A)  8274 acres 
B)  4913 acres 
C)  3411 acres 
D)  3593 acres

Question 18

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log _{8} 0.711$

Accepted Answer

A)  -0.1481 
B)  -0.1640 
C)  11.2518 
D)  -6.0966 
A)  -0.1481 
B)  -0.1640 
C)  11.2518 
D)  -6.0966

Question 19

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=7 x-3, g(x)=4 x-7$
Find $(f+g)(x)$.

Accepted Answer

A)  $-3 \mathrm{x}-4$ 
B)  $11 x+4$ 
C)  $11 \mathrm{x}-10$ 
D)  $3 \mathrm{x}-10$ 
A)  $-3 \mathrm{x}-4$ 
B)  $11 x+4$ 
C)  $11 \mathrm{x}-10$ 
D)  $3 \mathrm{x}-10$

Question 20

Use the horizontal-line test to determine whether the function is one to one.
-

Accepted Answer

A) True 
 B)False

Solve. - $4^{12-2 x}=4096$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=\frac{9 x-5}{2 x-7}$

Solve. - $\log _{2} 16=\mathrm{x}$

Solve the problem. -Find (f - g)(4) when $f(x)=3 x^{2}+5$ and $g(x)=x+1$ .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-5 x+8, g(x)=x^{2}-3 x-9$ Find $(f+g)(x)$ .

Solve. -The population of a small country increases according to the function $B=1,300,000 e^{0.04 t}$ , where $t$ is measured in years. How many people will the country have after 6 years?

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-7 x+5, g(x)=-2 x+7$ Find $(f+g)(x)$ .

Solve. - $4^{2 \mathrm{x}-18}=\frac{1}{16}$

Use the horizontal-line test to determine whether the function is one to one. -

Solve. - $(\log 3 x)^{2}+2 \log 3 x-8=0$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{b} y^{3}$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _{8.3} 2.9$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5$ Find $(f \cdot g)(x)$ .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-8 x+8, g(x)=-5 x+9$ Find $(\mathrm{f}-\mathrm{g})(\mathrm{x})$ .

Evaluate the given function - $\mathrm{f}(\mathrm{x})=4^{\mathrm{x}}, \mathrm{f}(4)$

Solve. -The number of acres in a landfill is given by the function $B=6500 e^{-0.04 t}$ , where $t$ is measured in years. How many acres will the landfill have after 7 years? (Round to the nearest acre.)

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _{8} 0.711$

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=7 x-3, g(x)=4 x-7$ Find $(f+g)(x)$ .

Use the horizontal-line test to determine whether the function is one to one. -

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

Solve. - 412−2x=40964^{12-2 x}=4096412−2x=4096

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=9x−52x−7f(x)=\frac{9 x-5}{2 x-7}f(x)=2x−79x−5​

Solve. - log⁡216=x\log _{2} 16=\mathrm{x}log2​16=x

Solve the problem. -Find (f - g)(4) when f(x)=3x2+5f(x)=3 x^{2}+5f(x)=3x2+5 and g(x)=x+1g(x)=x+1g(x)=x+1 .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - f(x)=−5x+8,g(x)=x2−3x−9f(x)=-5 x+8, g(x)=x^{2}-3 x-9f(x)=−5x+8,g(x)=x2−3x−9 Find (f+g)(x)(f+g)(x)(f+g)(x) .

Solve. -The population of a small country increases according to the function B=1,300,000e0.04tB=1,300,000 e^{0.04 t}B=1,300,000e0.04t , where ttt is measured in years. How many people will the country have after 6 years?

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - f(x)=−7x+5,g(x)=−2x+7f(x)=-7 x+5, g(x)=-2 x+7f(x)=−7x+5,g(x)=−2x+7 Find (f+g)(x)(f+g)(x)(f+g)(x) .

Solve. - 42x−18=1164^{2 \mathrm{x}-18}=\frac{1}{16}42x−18=161​

Use the horizontal-line test to determine whether the function is one to one. -

Solve. - (log⁡3x)2+2log⁡3x−8=0(\log 3 x)^{2}+2 \log 3 x-8=0(log3x)2+2log3x−8=0

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡by3\log _{b} y^{3}logb​y3

Evaluate using the change-of-base formula. Round to four decimal places. - log⁡8.32.9\log _{8.3} 2.9log8.3​2.9

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) or (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) as indicated. - f(x)=4x2+2x+4,g(x)=x2−4x+5f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5f(x)=4x2+2x+4,g(x)=x2−4x+5 Find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - f(x)=−8x+8,g(x)=−5x+9f(x)=-8 x+8, g(x)=-5 x+9f(x)=−8x+8,g(x)=−5x+9 Find (f−g)(x)(\mathrm{f}-\mathrm{g})(\mathrm{x})(f−g)(x) .

Evaluate the given function - f(x)=4x,f(4)\mathrm{f}(\mathrm{x})=4^{\mathrm{x}}, \mathrm{f}(4)f(x)=4x,f(4)

Solve. -The number of acres in a landfill is given by the function B=6500e−0.04tB=6500 e^{-0.04 t}B=6500e−0.04t , where ttt is measured in years. How many acres will the landfill have after 7 years? (Round to the nearest acre.)

Evaluate using the change-of-base formula. Round to four decimal places. - log⁡80.711\log _{8} 0.711log8​0.711

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - f(x)=7x−3,g(x)=4x−7f(x)=7 x-3, g(x)=4 x-7f(x)=7x−3,g(x)=4x−7 Find (f+g)(x)(f+g)(x)(f+g)(x) .

Use the horizontal-line test to determine whether the function is one to one. -

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

Solve. - $4^{12-2 x}=4096$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=\frac{9 x-5}{2 x-7}$

Solve. - $\log _{2} 16=\mathrm{x}$

Solve the problem. -Find (f - g)(4) when $f(x)=3 x^{2}+5$ and $g(x)=x+1$ .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-5 x+8, g(x)=x^{2}-3 x-9$ Find $(f+g)(x)$ .

Solve. -The population of a small country increases according to the function $B=1,300,000 e^{0.04 t}$ , where $t$ is measured in years. How many people will the country have after 6 years?

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-7 x+5, g(x)=-2 x+7$ Find $(f+g)(x)$ .

Solve. - $4^{2 \mathrm{x}-18}=\frac{1}{16}$

Solve. - $(\log 3 x)^{2}+2 \log 3 x-8=0$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{b} y^{3}$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _{8.3} 2.9$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5$ Find $(f \cdot g)(x)$ .

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-8 x+8, g(x)=-5 x+9$ Find $(\mathrm{f}-\mathrm{g})(\mathrm{x})$ .

Evaluate the given function - $\mathrm{f}(\mathrm{x})=4^{\mathrm{x}}, \mathrm{f}(4)$

Solve. -The number of acres in a landfill is given by the function $B=6500 e^{-0.04 t}$ , where $t$ is measured in years. How many acres will the landfill have after 7 years? (Round to the nearest acre.)

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _{8} 0.711$

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=7 x-3, g(x)=4 x-7$ Find $(f+g)(x)$ .