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Question

Find gof and fog, if (i) f(x)=|x| and g(x)=|5x2|

ii)f(x)=8x3 and g(x)=x13

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Solution

(i) f(x)=|x| and g(x)=|5x2|

(gof)(x)=g(f(x))=g(|x|)=|5|x|2|

And (fog)(x)=f(g(x))=f(|5x2|)=||5x2||=|5x2|
(ii)f(x)=8x3 and g(x)=x13

(gof)(x)=g(f(x))=g(8x3)=(8x3)13=2x

And (fog)(x)=f(g(x))=f(x13)=8(x13)3=8x

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