Find gof and fog, if
- f(x)=IxI and g(x)=I5x-2I
- f(x)=8x3 and g(x)=x1/3
- f(x)=IxI and g(x)=I5x-2I
- f(x)=8x3 and g(x)=x1/3
Solution and Explanation
(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.
(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
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