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Find the domain of the range of each of ...

Find the domain of the range of each of the following real functions:
`f(x)=(x-3)/(2-x)`

Text Solution

Verified by Experts

The correct Answer is:
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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