The domain of definition of the function `f(x) = sqrt(3-2^(x) -2^(1-x)) + sqrt(sqrt(sin^(-1)x,)` is

Options

A. `[0, 1]`
B. ` (0, 1]`
C. `[0, 1]`
D. none of these

Answer

A

Explanation

For f(x) to be real, we must have `3-2^(x) - 2^(1-x) ge 0 and sin^(-1) x ge 0`
`rArr 3.2^(x) -(2^(x))^(2) - 2 gt 0 and 0 le x le 1`
`rArr (2^(x))^(2) -3.2^(x) + 2 le 0 and 0 le x le 1`
`rArr 0 le x le 1 rArr in [0,1]`
Hence,domina `f(x) =[0,1]`