Choose the correct answer from the given four options. Let f : [2… - Vidyadip

MCQ

Choose the correct answer from the given four options. Let $f : [2, \infty ) \rightarrow R$ be the function defined by $f(x) = x^2– 4x + 5$, then the range of $f$ is:

A
$\text{R}$
✓
$[1,\infty)$
C
$[4,\infty)$
D
$[5,\infty)$

✓

Answer

Correct option: B.

$[1,\infty)$

Given that, $\text{f}(\text{x})=\text{x}^2-4\text{x}+5,$
Let $\text{y}=\text{x}^2-4\text{x}+5$
$\Rightarrow\ \text{y}=\text{x}^2-4\text{x}+4+1$
$=(\text{x}-2)^2+1$
$\Rightarrow\ (\text{x}-2)^2=\text{y}-1$
$\Rightarrow\ \text{x}-2=\sqrt{\text{y}-1}$
$\Rightarrow\ \text{x}=2+\sqrt{\text{y}-1}$
$\therefore\ \text{y}-1\geq0,\ \text{y}\geq1$
Range $=[1,\infty)$

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