The largest interval lying in `(-(pi)/(2), (pi)/(2))` for which the function `f(x)=4^(-x^(2))+cos^(-1)((x)/(2)-1)+log(cosx)` is defined, is :

Options

A. `[- pi//4, 2)`
B. `[ 0, pi//2)`
C. `[0, pi]`
D. ` (-pi//2, pi//2)`

Answer

B

Explanation

Clearly, `4^(-x^(2))` is defined for all `x in R` and `cos^(-1)((x)/(2)-1)` is defined for `-1 le (x)/(2) - 1 le 1`
i.e., for `0 le (x)/(2) le 2` or, `x in [0,4]`
Also ,log cos x is defined for all `x in (-pi//2,pi//2)`
`therefore f(x)` is defined for all `x in (-(pi)/(2),(pi)/(2)) nn[0,4]nnR = [0,(pi)/(2))`