What are the sum and difference of the identity function and the recip – InterviewSolution

InterviewSolution

1.	What are the sum and difference of the identity function and the reciprocal function ?
Answer» Let `f:RtoR:f(x)=xandg:R-{0}toR:g(x)=(1)/(x)` be the identity function and the reciprocal function respectively. Then, dom `(f)nn"dom "(g)=RnnR-{0}=R-{0}`. `:.(f+g):R-{0}toR:(f+g)(x)=f(x)+g(x)=(x+(1)/(x))`. Hence, `(f+g)(x)=(x+(1)/(x))"for all "x""inR-{0}`. And, `(f-g):R-{0}toR:(f-g)(x)=f(x)-g(x)=(x-(1)/(x))`. Hence, `(f-g)(x)=(x-(1)/(x))"for all "x""inR-{0}`.

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