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  4. The domain of the function f(x) = sin-1((x+5/2)) is

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Q. The domain of the function $f\left(x\right) = sin^{-1}\left(\frac{x+5}{2}\right)$ is

KEAMKEAM 2012Inverse Trigonometric Functions

Solution:

Given, $f(x)=\sin ^{-1}\left(\frac{x+5}{2}\right)$
$\left[\because\right.$ Domain of $\sin ^{-1} x$ is $\left.x \in[-1,1]\right]$
$\therefore $ For $f(x)$ to be defined
$ -1 \leq \frac{x+5}{2} \leq 1 $
$ \Rightarrow -2 \leq x+5 \leq 2 $
$ \Rightarrow -2-5 \leq x \leq 2-5$
$ \Rightarrow -7 \leq x \leq-3 $
$ \therefore x \in[-7,-3] $