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Question

If the function f:RR be given by f(x)=x2+2 and g:RR be given by g(x)=xx1,x1,
find fog and gof and hence fing fog(2) and gof(-3).

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Solution

We have fog(x)=f[g(x)]=f(xx1)=(xx1)2+2

And, fog(2)=(221)2+2=6

Also, gof(x)=g[f(x)]=g(x2+2)=x2+2x2+21=x2+2x2+1

And, gof(3)=(3)2+2(3)2+1=1110


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