The function f: [0, ∞) → R defined by, f(x) = 2x^2 + 3, is

The correct answer is Option (2) → one-one but not onto

$f:[0,\infty)\to \mathbb{R}$, $f(x)=2x^{2}+3$

Check one-one:

$f'(x)=4x \ge 0$ for $x\ge 0$

Strictly increasing ⇒ one-one.

Check onto:

For $x\ge 0$, $2x^{2}+3 \ge 3$.

So the range is $[3,\infty)$, not all $\mathbb{R}$.

Hence not onto.

Answer: one-one but not onto