Find the sum and product of identity function and the modulus function – InterviewSolution

InterviewSolution

1.	Find the sum and product of identity function and the modulus function.
Answer» Let `f:RtoR:f(x)=xandg:RtoR:g(x)=\|x\|` be the identity function and the modulus function respectively. Then, dom `(fg)="dom "(f)nn"dom "(g)=RnnR=R`. `(fg):RtoR:(fg)(x)=f(x).g(x)`. Now, `(fg)(x)=f(x),g(x)=x.\|x\|` `=x.{{:(x",when "xge0),(-x" ,when "lt0):}={{:(x^(2)",when "xge0),(-x^(2)",when "xlt0):}` Hence, `(fg)(x)={{:(x^(2)",when "xge0),(-x^(2)",when "xlt0):}`.

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