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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)=(3x-2)/(x+2)`

Text Solution

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The correct Answer is:
dom `(f)=R-{-2}," range "(f)=R-{3}`
`f(x)=(3x-2)/(x+2)` not defined when x=-2. So, dom `(f)=R-{-2}`.
Let y=f(x). Then,
`y=(3 x-2)/(x+2)impliesxy+2y=3x-2implies3x-xy=2y+2`
`impliesx(3-y)=2y+2impliesx=(2y+2)/(3-y)." "....(i)`
It follows from (i) that x is not defined when y=3.
`:." range "(f)=R-{3}`.
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