Find the domain and the range of the real function, `f(x)=(x-3)/(x-5)` – InterviewSolution

InterviewSolution

1.	Find the domain and the range of the real function, `f(x)=(x-3)/(x-5)`.
Answer» We have, `f(x)=(x-3)/(x-5)`. Clearly, f(x) is defined for all real values of x except that at which `x-5=0,i.e.,x=5`. `:."dom"(f)=R-{5}` Let `y=f(x)`. Then, `y=(x-3)/(x-5)impliesxy-5y=x-3` `impliesx(y-1)=5y-3impliesx=(5y-3)/(y-1)." "....(i)` It is clear from (i) that x is not defined when y-1=0, i.e., when y=1. `:."range"(f)=R-{1}`. Hence, dom `(f)=R-{5}" and range "(f)=R-{1}`.

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