If `g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2` , then (a). `f(x)=sin^2x ,g(x)=sqrt(x)` (b). `f(x)=sinx ,g(x)=|x|` (c). `f(x=x^2,g(x)=sinsqrt(x)` (d).`f\ a n d \g` cannot be determined

Options

A. `f(x)=sin^(2)x, g(x)=sqrtx`
B. `f(x)=sinx, g(x)=|x|`
C. `f(x)=x^(2),g(x)=sinsqrtx`
D. f and g cannot be determined

Answer

A

Explanation

We have,
`f(g(x))=(sin sqrtx)^(2)and,g(f(x))=|sinx|=sqrt(sin^(2)x)`
`Rightarrow g(x)=sqrtx and f(x)=(sin x)^(2)`