The largest interval lying in `(-pi/2,pi/2)` in which the function `f(x) = 3^(-x^2) + arc cos(1/2x-1)+logcosx`, is defined, is

Options

A. `[0, π]`
B. `[-pi/2,pi/2]`
C. `[0,pi/2)`
D. none of these

Answer

C

Explanation

(c) is defined for all `x in R`
arc `cos (1/2x -1)` is defined for
`−1 lt= x − 1 lt= 1 i.e., 0 lt= x lt= 4`
and log cos x is defined (real) for
`cos x gt 0 i.e., 2n pi − pi/2 lt x lt 2n pi + pi/2`
Hence the largest interval lying in
`(−pi/2, pi/2)` is `[0, pi/2)`.