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If f : R rarr R and g : R rarr R be two ...

If `f : R rarr R and g : R rarr R` be two mapping such that f(x) = sin x and g(x) = `x^(2)`, then
prove that fog `ne` gof.

Text Solution

Verified by Experts

(fog) (x) = f[(g(x)]
= `f(x^(2)) = sin x^(2)`Ans.
and (gof)(x)= g[f(x)]
=g(sinx) = `(sinx)^(2)= sin^(2) x` Ans.
Therefore, fog `ne` gof . Hence Proved.
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