Question

For the function, $f\left(x\right)=ta{n}^{-1}x+si{n}^{-1}x+co{s}^{-1}x$

• A. Domain is $xϵR$
• B. Domain is $xϵ[-1,1]$
• C. Range is $(0,\pi )$
• D. Range is $[\frac{\pi }{4},\frac{3\pi }{4}]$

Answer 1

Answer: (B), (D)

The correct options are
B Domain is $xϵ[-1,1]$
D Range is $[\frac{\pi }{4},\frac{3\pi }{4}]$

$f\left(x\right)=ta{n}^{-1}x+si{n}^{-1}x+co{s}^{-1}x$
Common domain is $xϵ[-1,1]$
$\therefore f\left(x\right)=ta{n}^{-1}x+\frac{\pi }{2}$
$f(-1)=-\frac{\pi }{4}+\frac{\pi }{2}=\frac{\pi }{4}$
$f\left(1\right)=\frac{\pi }{4}+\frac{\pi }{2}=\frac{3\pi }{4}$