1.

Find the domain of the range of each of the following real functions: `f(x)=1-|x-2|`

Answer» Correct Answer - dom `(f)=R," range "(f)=(-oo,1]`
`f(x)=1-|x-2|` is defined for all `x""inR`. So, dom (f)=R.
Now, `0le|x-2|ltooimplies|x-2|ge0and|x-2|ltoo`
`implies-|x-2|le0and-|x-2|gt-oo`
`implies1-|x-2|le0and-|x-2|gt-oo`
`implies-oolt1-|x-2|le1impliesf(x)in(-oo,1]`.
`:."range "(f)=(-oo,1]`.


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