Question

Find gof and fog, if

1. f(x)=IxI and g(x)=I5x-2I
2. f(x)=8x3 and g(x)=x1/3

Answer 1

(i)f(x)=IxI and g(x)=I5x-2I

therefore (gof)(x)=g(f(x))=g(IxI)=I5IxI-2I
(fog)(x)=f(g(x))=f(I5x-2I)=II5x-2II=I5x-2I.

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(ii)f(x)=8x3 and g(x)=x1/3

therefore (gof)(x)=g(f(x))=g(8x3)=(8x3)1/3=2x
(fog)(x)=f(g(x))=f(x 1/3)=8(x 1/3)3=8x