Find range of `f(x)=(x-3)/(4-x).`

Options

A. R
B. R-{1}
C. R-{-1}
D. None of these

Answer

C

Explanation

Let `f(x)=(x-3)/(4-x)`
Domain of the function :
f (x) is defined if `4-xne0`
`implies" "xne4`
`therefore"Domain of"" "f(x)=R-4{4}. `
Range of function, Let y = f (x)
`implies" "y=(x-3)/(4-x)`
`implies" " 4y-xy=x-3`
`implies" "4y-+3=x(1+y)`
`implies" "x=(4y+3)/(1+y)`
which is not defined at y = -1
`therefore` Range of function =R -{-1}.