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The domain and range of the function f g...

The domain and range of the function f given by` f(x) =2 - |x-5|` is

A

Domain =`R^(+)`, Range =`(-oo,1]`

B

Domain =R, Range =`(-oo,2]`

C

Domain =R, Range =`(-oo,2)`

D

Domain =`R^(+)`, Range =`(-oo,2]`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, f(x)=2-|x-5|
f(x) is defined for all `x in R`
`:.` Domain of f=R
We know, that, `|x-5|ge0rArr-|x-5|le0`
`rArr 2-|x-5|le2`
`:. f(x) le2`
`:.` Range of `f=[-oo,2]`
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