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  4. The function f(x)= cot -1 √(x+3) x+ cos -1 √x2+3 x+1 is defined on the set S, where S=

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Q. The function $f(x)=\cot ^{-1} \sqrt{(x+3) x}+\cos ^{-1} \sqrt{x^2+3 x+1}$ is defined on the set $S$, where $S=$

Inverse Trigonometric Functions

Solution:

$ x ( x +3) \geq 0 \Rightarrow x \geq 0 \text { or } x \leq-3 $
$\text { and } -1 \leq x^2+3 x+1 \leq 1 \Rightarrow x(x+3) \leq 0 $
$\text { Hence }-3 \leq x \leq 0$
$\text { Hence } x =0 \text { or }-3 \Rightarrow x =\{0,-3\}$