Question

Find the product of the identitly function by the reciprocal function.

Answer 1

Let `f:RtoR:f(x)=xandg:R-{0}toR:g(x)=(1)/(x)` be the identity function and the reciprocal function respectively.
Then, dom `(fg)="dom "(f)nn"dom "(g)=RnnR-{0}=R-{0}`
`:.(fg):Rto{0}toR:f(g)(x)=f(x).g(x)=(x""xx(1)/(x))=1`.
Hence, `(fg)(x)=1" for all "x""inR-{0}`.