Find the domain and the range of the function, `f(x)=(x-2)/(x-3)`. – InterviewSolution

InterviewSolution

1.	Find the domain and the range of the function, `f(x)=(x-2)/(x-3)`.
Answer» We have, `f(x)=(x-2)/(x-3)` Clearly, f(x) is defined for all real values of x for which `x-3ne0`, i.e., `xne3`. `:."dom "(f)=R-{3}`. Let y=f(x). Then, `y=(x-2)/(x-3)impliesxy-3y=x-2` `impliesx(y-1)=3y-2` `impliesx=(3y-2)/(y-1)." "....(i)` It follows from (i) that x assumes real values for all y except that for which y-1=0, i.e., y=1. `:."range "(f)=R-{1}`. Hence, dom `(f)=R-{3}"and range "(f)=R-{1}`.

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