Composite and inverse functions Quiz

1. $f(x)=2x+1$ and $g(x)=x^2$. Find $gf(3)$.

• A. $19$
• B. $49$
• C. $7$
• D. $13$

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

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

3. $f(x)=x^2$ for $x\le0$. Which is $f^{-1}(x)$?

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

4. $f(x)=\sqrt{x}$ for $x\ge0$ has range $y\ge0$. What is the domain of $f^{-1}$?

• A. $x\le0$
• B. all real $x$
• C. $x>0$ only
• D. $x\ge0$

5. $f(x)=2x+3$. Given $f^{-1}(a)=4$, what is $a$?

• A. $11$
• B. $5.5$
• C. $-0.5$
• D. $2$