Find fog and gof:f(x)=3 x-2, g(x)=x^2 - Vidyadip

Question

Find fog and gof:$f(x)=3 x-2, g(x)=x^2$

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Answer

$ f(x)=3 x-2, g(x)=x^2$
$\text { (fog) }(x)=f(g(x))=f\left(x^2\right)=3 x^2-2$
$\text { (gof) }(x)=g(f(x))$
$=g(3 x-2)$
$=(3 x-2)^2$
$=9 x^2-12 x+4$

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