Find the domain of the range of each of the following real functions: – InterviewSolution

InterviewSolution

1.	Find the domain of the range of each of the following real functions: `f(x)=(x-3)/(2-x)`
Answer» Correct Answer - dom `(f)=R-{2}," range "(f)=R-{-1}` `f(x)=(x-3)/(2-x)` is not defined when x=2. So, dom `(f)=R-{2}`. Let y=f(x). Then, `y=(x-3)/(2-x)implies2y-xy=x-3impliesxy+x=2y+3` `impliesx(y+1)=2y+3impliesx=(2y+3)/(y+1)`. `:.` x is not defined when y=-1. So, range `(f)=R-{-1}`

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