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Question

Find the product of the identity function by the modulus function.

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Solution

Let f:RR:f(x)=x and g:RR:g(x)=|x| be the identity function and the modulus function respectively.

Then, dom (fg)=dom (f)dom (g)=RR=R

(fg):RR:(fg)(x)=f(x).g(x)

Now, (fg)(x)=f(x).g(x)=x.|x|

=x.{x, when x0x, when x<0={x2, when x0x2, when x<0

Hence, (fg)(x)={x2, when x0x2, when x<0


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