Composite and inverse functions Quiz

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

• A. $49$
• B. $15$
• C. $19$
• D. $7$

2. Find $f^{-1}(x)$ for $f(x)=3x-5$.

• A. $\frac{x+5}{3}$
• B. $\frac{x-5}{3}$
• C. $\frac{1}{3x-5}$
• D. $3x+5$

3. Which function has no inverse on the domain given?

• A. $f(x)=x^3$, $x\in\mathbb{R}$
• B. $f(x)=x^2$, $x\in\mathbb{R}$
• C. $f(x)=x^2$, $x\geq0$
• D. $f(x)=e^x$, $x\in\mathbb{R}$

4. $f(x)=x^2+2$, $x\geq0$. State the domain of $f^{-1}$.

• A. $x\geq0$
• B. $x\leq2$
• C. $x\in\mathbb{R}$
• D. $x\geq2$

5. The point $(2,7)$ lies on $y=f(x)$. Which point lies on $y=f^{-1}(x)$?

• A. $(2,7)$
• B. $(-2,7)$
• C. $(7,2)$
• D. $(-7,-2)$