Question

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

• A. Domain is
• B. Domain is
• C. Range is
• D. Range is

Answer 1

Answer: (B), (D)

The correct options are
B

Domain is

D

Range is

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

common domain is $x\in [-1,1]$

$\therefore f\left(x\right)=ta{n}^{-1}x+\frac{\pi }{2}$

$f(-1)=-\frac{\pi }{4}+\frac{\pi }{2}=\frac{\pi }{4}$

$f\left(1\right)=\frac{\pi }{4}+\frac{\pi }{2}=\frac{3\pi }{4}$