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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-4|)/(x-4)`

Text Solution

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The correct Answer is:
dom `(f)=R-{4}," range "(f)={-1,1}`
`f(x)=(|x-4|)/(x-4)` is not defined at x=4. So, dom `(f)=R-{4}`.
Now, when `xne4`, we have
`f(x)={{:(1",""when "x-4gt0 ,[:'|x-4|=x-4}),(1-",when "x-4lt0 ,[:'|x-4|=-(x-4)}):}`
`:."range "(f)=(-1,1]`.
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