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The domain and range of the real functio...

The domain and range of the real function f defined by `f(x)=(4-x)/(x-4)` is

A

Domain =R , Range ={-1,2}

B

Domain =R -{1}, Range R

C

Domain =R -{4}, Range ={-1}

D

Domain =R -{-4}, Range ={-1,1}

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `f(x) =(4-x)/(x-4)`
f(x) is defined, if `x-4 ne 0i.e.,xne4`
`:.` Domain of f=R-{4}
Let f(x)=y
`:. Y=(4-x)/(x-4)rArrxy-4y=4-x`
`rArr xy+x=4+4yrArrx(y+1)=4(1+y)`
`:. x=(4(1+y))/(y+1)`
x assumes real values, if, `y+1 ne0.i.e.,y=1`
`:.` Range of f=R-{-1}`
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