1.

If `g(f(x))=|sinx|` and `f(g(x))=(sin(sqrtx))^2` thenA. `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» Correct Answer - A
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)`


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