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204 Chapter 3 Exponential and Logarithmic Functions<br />
83. f has an inverse because f is one-to-one.<br />
y 5x 7<br />
x 5y 7<br />
x 7 5y<br />
f 1 x 1 5x 7<br />
84. f is one-to-one, so it has an inverse.<br />
f x 2 3 x 5 2<br />
y 2 3 x 5 2<br />
x 2 3 y 5 2<br />
x 5 2 2 3 y<br />
3 2x 5 2 y<br />
f 1 x 3 2 x 15 4<br />
85. f has an inverse because f is one-to-one.<br />
86. f is not one-to-one, so it does not have an inverse.<br />
y 3 x 8<br />
x 3 y 8<br />
x 3 y 8<br />
x 3 8 y<br />
f 1 x x 3 8<br />
87.<br />
f x <br />
2x<br />
x 7<br />
Vertical asymptote: x 7<br />
Horizontal asymptote: y 2<br />
Intercept: 0, 0<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
−4 −2<br />
y<br />
6<br />
8 10 12 14 16<br />
x<br />
−4<br />
−6<br />
−8<br />
88.<br />
f x x2 3<br />
x 1 x 1 4<br />
x 1<br />
y<br />
Slant asymptote: y x 1<br />
Vertical asymptote: x 1<br />
Intercept: 0, 3<br />
89. Answers will vary.<br />
−10 −8 −6 −4 −2<br />
2<br />
2<br />
4<br />
6<br />
8 10<br />
x<br />
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