Inverse functions and their graphs Quiz

1. Find $f^{-1}(x)$ for $f(x)=3x-4$.

• A. $\frac{x}{3}+4$
• B. $\frac{3}{x-4}$
• C. $\frac{x-4}{3}$
• D. $\frac{x+4}{3}$

2. $f$ has domain $x\geqslant1$ and range $f(x)\geqslant5$. What is the domain of $f^{-1}$?

• A. $x\geqslant5$
• B. $x\geqslant1$
• C. $x\leqslant5$
• D. $x\in\mathbb{R}$

3. What is the inverse of $f(x)=x^2$, $x\geqslant0$?

• A. $-\sqrt{x}$
• B. $\frac{1}{x^2}$
• C. $\sqrt{x}$
• D. $\pm\sqrt{x}$

4. The graph of $y=f^{-1}(x)$ is the reflection of $y=f(x)$ in which line?

• A. the $x$-axis
• B. $y=x$
• C. the $y$-axis
• D. $y=-x$

5. Which function is self-inverse?

• A. $f(x)=x+1$
• B. $f(x)=2x$
• C. $f(x)=x^2$, $x\geqslant0$
• D. $f(x)=\frac1x$, $x\neq0$