The range of the function f ( x )=3-x+2+x is - Vidyadip

MCQ

The range of the function $f ( x )=\sqrt{3-x}+\sqrt{2+x}$ is

✓
$[\sqrt{5}, \sqrt{10}]$
B
$[2 \sqrt{2}, \sqrt{11}]$
C
$[\sqrt{5}, \sqrt{13}]$
D
$[\sqrt{2}, \sqrt{7}]$

✓

Answer

Correct option: A.

$[\sqrt{5}, \sqrt{10}]$

a
$y^2=3-x+2+x+2 \sqrt{(3-x)(2+x)}$

$=5+2 \sqrt{6+x-x^2}$

$y^2=5+2 \sqrt{\frac{25}{4}-\left(x-\frac{1}{2}\right)^2}$

$y_{\max }=\sqrt{5+5}=\sqrt{10}$

$y_{\min }=\sqrt{5}$

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