The domain of the function f(x)= ^ -1 ( x^ 2 -3 x+2 x^ 2 +2 x+7 )… - Vidyadip

MCQ

The domain of the function $f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$ is.

A
$[1, \infty)$
B
$(-1,2]$
✓
$[-1, \infty)$
D
$(-\infty, 2]$

✓

Answer

Correct option: C.

$[-1, \infty)$

c
$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$ Domain

$\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \geq-1$ and $\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1$

$2 x^{2}-x+9 \geq 0$ and $5 x \geq-5 \Rightarrow x \geq-1$ $x \in R$

Hence Domain $x \in[-1, \infty)$

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