Question 1

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

Accepted Answer

A)  $\frac{2}{(x-5)^{2}}$, all real numbers exœpt 5 
B)  $\frac{2}{x^{2}-5}$, all real numbers except $\sqrt{5}$ 
C)  $\frac{2}{x^{2}}-5$, all real numbers except 0 
D)  $\frac{-3}{x^{2}}$, all real numbers except 0 
A)  $\frac{2}{(x-5)^{2}}$, all real numbers exœpt 5 
B)  $\frac{2}{x^{2}-5}$, all real numbers except $\sqrt{5}$ 
C)  $\frac{2}{x^{2}}-5$, all real numbers except 0 
D)  $\frac{-3}{x^{2}}$, all real numbers except 0

Question 2

Solve.
-$\ln x=1$

Accepted Answer

A)  No solution 
B)  $\{\mathrm{e}\}$ 
C)  $\{1\}$ 
D)  $\{0\}$ 
A)  No solution 
B)  $\{\mathrm{e}\}$ 
C)  $\{1\}$ 
D)  $\{0\}$

Question 3

For the given function $f(x)$, find $f^{-1}(x)$. State the domain of $f^{-1}(x)$.
-$f(x)=\sqrt{x}-8$

Accepted Answer

A)  $f^{1}(x)=(x-8)^{2}, x \geq-8$ 
B)  $f^{-1}(x)=(x+8)^{2}, x \geq-8$ 
C)  $f 1(x)=-(x+8)^{2}, x \geq-8$ 
D)  $f^{-1}(x)=x+8, x \geq-8$ 
A)  $f^{1}(x)=(x-8)^{2}, x \geq-8$ 
B)  $f^{-1}(x)=(x+8)^{2}, x \geq-8$ 
C)  $f 1(x)=-(x+8)^{2}, x \geq-8$ 
D)  $f^{-1}(x)=x+8, x \geq-8$

Question 4

Rewrite in exponential form.
-$\log _{4} 64=3$

Accepted Answer

A)  $3^{4}=64$ 
B)  $4^{3}=64$ 
C)  $4^{64}=3$ 
D)  $64^{3}=4$ 
A)  $3^{4}=64$ 
B)  $4^{3}=64$ 
C)  $4^{64}=3$ 
D)  $64^{3}=4$

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

Solve. - $\ln x=1$

For the given function $f(x)$ , find $f^{-1}(x)$ . State the domain of $f^{-1}(x)$ . - $f(x)=\sqrt{x}-8$

Rewrite in exponential form. - $\log _{4} 64=3$

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)=2x2;g(x)=x−5f(x)=\frac{2}{x^{2}} ; g(x)=x-5f(x)=x22​;g(x)=x−5 Find (g∘f)(x)(\mathrm{g} \circ \mathrm{f})(\mathrm{x})(g∘f)(x) .

Solve. - ln⁡x=1\ln x=1lnx=1

For the given function f(x)f(x)f(x) , find f−1(x)f^{-1}(x)f−1(x) . State the domain of f−1(x)f^{-1}(x)f−1(x) . - f(x)=x−8f(x)=\sqrt{x}-8f(x)=x​−8

Rewrite in exponential form. - log⁡464=3\log _{4} 64=3log4​64=3