Range of the function `f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x))` is equal to

Options

A. `(0,(pi)/(2)+sqrt((pi)/(2))]`
B. `[(pi)/(2),(pi)/(2)+sqrt((pi)/(2))]`
C. `[(pi)/(6),(pi)/(2)]`
D. `{(pi)/(6)}`

Answer

D

Explanation

We have `f(x)=sqrt(-sin^(-1)(sqrtlog_(4)x))+sin^(-1)((1+x^(4))/(4x))`
Clearly, domain of `f(x)` is `x=1` only, so `f(1)=sqrt0+sin^(-1)((2)/(4))=(pi)/(6).`
Hence, range of f(x) is `{(pi)/(6)}.`