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Let f: RrarrR and g: RrarrR be two fun...

Let `f: RrarrR` and `g: RrarrR` be two functions such that `fog(x)=sinx^2a n dgof(x)=sin^2x` Then, find `f(x)a n dg(x)dot`

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Given, `(fog)(x) = sin x^2 and (gof)(x) = sin^2 x`

` f(g(x)) = sin(x^2) & g(f(x)) = (sin x)^2` ...(1)

Clearly, `f(x) = sin x & g(x) = x^2` satisfies both conditions of (1)

So,`f(x) = sin x and f(x) = x^2`
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