1.

The domain and range of the real function f defined by `f(x)=(4-x)/(x-4)` isA. Domain =R , Range ={-1,2}B. Domain =R -{1}, Range RC. Domain =R -{4}, Range ={-1}D. Domain =R -{-4}, Range ={-1,1}

Answer» Correct Answer - 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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