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The largest interval lying in (-pi/2,pi/...

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 (1) `[0,pi]` (2) `(-pi/2,pi/2)` (3) `[-pi/4,pi/2)` (4) `[0,pi/2)`

Text Solution

Verified by Experts

`F(x)=4^(-x^2)+cos^-1(x/2-1)+log(cosx)`
`-1<=x/2-1<=1`
`0<=x/2<=2`
`0<=x<=4........(1)`
`log (cosx) when cosx>0`
`cos>0`
`x=(0,pi/2).....(2)`
final`x=(0,pi/2)`
...
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