Range of the function `f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x))` is equal to (A) `(0,pi/2+sqrt(pi/2)]` (B) `[pi/2,pi/2+sqrt(pi/2)]` (C) `[pi/6,pi/4)` (D) `{pi/6}`A. `(0,(pi)/(2)+sqrt((pi)/(2))]`B. `[(pi)/(2),(pi)/(2)+sqrt((pi)/(2))]`C. `[(pi)/(6),(pi)/(2)]`D. `{(pi)/(6)}`

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

1.	Range of the function `f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x))` is equal to (A) `(0,pi/2+sqrt(pi/2)]` (B) `[pi/2,pi/2+sqrt(pi/2)]` (C) `[pi/6,pi/4)` (D) `{pi/6}`A. `(0,(pi)/(2)+sqrt((pi)/(2))]`B. `[(pi)/(2),(pi)/(2)+sqrt((pi)/(2))]`C. `[(pi)/(6),(pi)/(2)]`D. `{(pi)/(6)}`
Answer» Correct Answer - D 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)}.`