Functions: domain, range and composition Quiz

1. $f(x)=3x-2$, $g(x)=x^2$. Find $\mathrm{fg}(2)$.

• A. $16$
• B. $4$
• C. $10$
• D. $6$

2. What is the range of $f(x)=(x-1)^2+4$, $x\in\mathbb{R}$?

• A. $f(x)\geqslant1$
• B. $f(x)\geqslant5$
• C. $f(x)\geqslant-4$
• D. $f(x)\geqslant4$

3. Which function is many-one on $\mathbb{R}$?

• A. $f(x)=2x+1$
• B. $f(x)=x^3$
• C. $f(x)=x^2$
• D. $f(x)=x-5$

4. What is the largest real domain of $\sqrt{x-3}$?

• A. $x\geqslant3$
• B. $x>3$
• C. $x\leqslant3$
• D. $x\in\mathbb{R}$

5. $f(x)=x+1$, $g(x)=2x$. Find $\mathrm{fg}(x)$.

• A. $2x+2$
• B. $2x+1$
• C. $2x^2$
• D. $x+2$