- Home
- Standard 12
- Mathematics
1.Relation and Function
normal
Domain of the function $f(x) = {\sin ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\cos ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right)$ is
A
$R$
B
$[0,6]$
C
$[-6,6]$
D
$[-3,3]$
Solution
$f(x)$ is defined, if
$-1 \leq \frac{2-|x|}{4} \leq 1 \text { and }-\infty<\frac{2-|x|}{4} < \infty$
$\Rightarrow-4 < 2-|x| \leq 1 \text { and } x \in R$
$\Rightarrow-6 \leq-|x| \leq 2 \text { and } x \in R$
$\Rightarrow-2 \leq|x| \leq 6 \text { and } x \in R$
$\Rightarrow|x| \leq 6 \text { and } x R \Rightarrow x \in[-6,6]$
$\text { Hence, domain }(f)=[-6,6]$
Standard 12
Mathematics
