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Question

Let f,g:RR be two functions defined as f(x)=|x|+x,g(x)=|x|x,xR. Then, find fg and gf.

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Solution

f(x)=|x|+x

g(x)=|x|x

fog(x)=f(g(x))=f(|x|x)

fog(x)=||x|x|+|x|x

And--

gof(x)=g(f(x))=g(|x|+x)

gof(x)=||x|+x||x|x

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