Question

Let $f:[2,\infty) \to R$ be the function defined $f(x) = x^2 - 4x + 5$ , then the range of f is

• A. $(-\infty, \infty)$
• B. $[1, \infty)$
• C. $(1, \infty)$
• D. $[5, \infty)$

Answer 1

Answer: (B)

$f(x)=(x-2)^{2}+1 \geq 1, \forall x \in[2, \infty)$
$f_{\min }=1$ at $x=2$
$\therefore $ Range of $f$ is $[1, \infty)$