Algebra and Trigonometry, 5th Edition

Mid-Chapter Mixed Review

Determine whether the statement is true or false.

1. The domain of all logarithmic functions is $[1,\infty )$. [5.3]

2. The range of a one-to-one function f is the domain of its inverse $f^{-1}$. [5.1]

3. The y-intercept of $f(x)=e^{-x}$ is (0, −1). [5.2]

For each function, determine whether it is one-to-one, and if the function is one-to-one, find a formula for its inverse. [5.1]

4. $f(x)=-\frac{2}{x}$

5. $f(x)=3+x^2$

6. $f(x)=\frac{5}{x-2}$

7. Given the function $f(x)=\sqrt{x-5}$, use composition of functions to show that $f^{-1}(x)=x^2+5$. [5.1]

8. Given the one-to-one function $f(x)=x^3+2$, find the inverse, give the domain and the range of f and $f^{-1}$, and graph both f and $f^{-1}$ on the same set of axes. [5.1]

Match the function with one of the graphs (a)–(h) that follow. [5.2], ...