Question
If $$g\left\{ {f\left( x \right)} \right\} = \left| {\sin \,x} \right|$$ and $$f\left\{ {g\left( x \right)} \right\} = {\left( {\sin \,\sqrt x } \right)^2}$$ then :
A.
$$f\left( x \right) = {\sin ^2}x,\,g\left( x \right) = \sqrt x $$
B.
$$f\left( x \right) = \sin \,x,\,g\left( x \right) = \left| x \right|$$
C.
$$f\left( x \right) = {x^2},\,g\left( x \right) = \sin \,\sqrt x $$
D.
$$f$$ and $$g$$ cannot be determined
Answer :
$$f\left( x \right) = {\sin ^2}x,\,g\left( x \right) = \sqrt x $$
Solution :
Verify by trial.