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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^(2)-16)/(x-4)`

Text Solution

Verified by Experts

The correct Answer is:
dom `(f)=R-{4}," range "(f)=R-{8}`
`f(x)=(x^(2)-16)/(x-4)` is not defined when x=4. So, dom `(f)=R-{4}`. Let y=f(x). Then,
`y=(x^(2)-16)/(x-4)=(x+4)," when "xne5`
`impliesyne(4+4)impliesyne8." So, range "(f)=R-{8}`.
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