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Question

If g f x=sin x and f g x=sin x2, then
(a) fx=sin2 x, gx=x
(b) fx=sin x, gx=|x|
(c) fx=x2, gx=sin x
(d) f and g cannot be determined.

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Solution

If we solve it by the trial-and-error method, we can see that (a) satisfies the given condition.
From (a):
fx=sin2x and gx=xfgx=fx=sin2 x=sin x2
So, the answer is (a).

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