If `f(x)=sin^2x` and the composite function `g(f(x))=|sinx|` , then `g(x)` is equal to `sqrt(x-1)` (b) `sqrt(x)` (c) `sqrt(x+1)` (d) `-sqrt(x)`

Explanation

given that,
`f(x)=sin^2x`
`g(f(x))=|sinx|`
`A: `Take `g(x)=sqrt(x-1)`
`=>g(f(x))=g[f(x)]`
`=g(sin^2x)`
`=sqrt(sin^2x-1)`
We can see, `g(x)=sqrt(x-1)` is not possible.
`B: `Take `g(x)=sqrtx`
`=>g(f(x))=g[f(x)]`
`=g(sin^2x)`
`=sqrt(sin^2x)`
`=pmsinx`
`=abs(sinx)`
` ` Here, we can see `g(x)=sqrtx`