Find the quotient of the identity function by the reciprocal function. – InterviewSolution

InterviewSolution

1.	Find the quotient of the identity function by the reciprocal function.
Answer» Let `f:RtoR:f(x)andg:R-{0}toR:g(x)=(1)/(x)` be the identity function and the reciprocal function respectively. Now, dom `((f)/(g))="dom "(f)nn"dom "(g)-{x:g(x)=0}` and `{x:g(x)=0}={x:(1)/(x)=0}=phi`. `:."dom "((f)/(g))=[RnnR-{0}]-phi=R-{0}` So, `(f)/(g):R-{0}toR:((f)/(g))(x)=(f(x))/(g(x))=(x)/((1)/(x))=x^(2)`. Hence, `((f)/(g))(x)=x^(2)"for all "x""inR-{0}`.

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