Define $f: \mathbb{R} o \mathbb{R}$ by $f(x) = x^{2}$. What is the *…

Question

Define $f: \mathbb{R} 	o \mathbb{R}$ by $f(x) = x^{2}$. What is the **range** of $f$?

Accepted Answer

C. $[0, \infty)$ (non-negative reals)

$x^{2} \ge 0$ for all real $x$, with equality iff $x = 0$. Every non-negative real value is attained (e.g., $y \ge 0 \Rightarrow x = \sqrt{y}$ works). So range $= [0, \infty)$.
- **B** excludes $0$ — but $f(0) = 0$ is in the range.

Answer

$\mathbb{R}$

Answer

$\mathbb{R}^{+}$ (positive reals only)

Answer

$\{0\}$

Define $f: \mathbb{R} \to \mathbb{R}$ by $f(x) = x^{2}$. What is the **range** of $f$?

Define $f: \mathbb{R} \to \mathbb{R}$ by $f(x) = x^{2}$. What is the range of $f$?