`f(x)=sqrt(e^(cos^(-1)(log_(4)x^(2))))`

Options

A. `[1//2, 2 ]`
B. `[-2, - 1//2] uu [1//2, 2]`
C. `[-2, - 1//2]`
D. none of these

Answer

B

Explanation

For f(x) to be real, we must have
`-1 le log_(4) x^(2) le 1 and x ne 0`
`rArr 4^(-1) le x^(2) le 4^(1) and x ne 0`
`rArr (1)/(4) x^(2) le 4 and x ne 0`
`rArr x in [-2,-1//2] uu [1//2,2] and ne 0`
`rArr x in [-2,-1//2] uu [1//2,2]`