# The domain and range of the real function of defined by f(x)=

Question:

The domain and range of the real function of defined by $f(x)=\frac{4-x}{x-4}$ is given by

(a) Domain = R, Range ={−1, 1}

(b) Domain = R −{1}, Range = R

(c) Domain = R −{4}, Range = {−1}

(d) Domain = R −{−4}, Range = {−1, 1}

Solution:

$f(x)=\frac{4-x}{x-4}$

Domain :- for $f(x)=\frac{4-x}{x-4}$

$x-4 \neq 0$

i.e $x \neq 4$

∴ Domain is R −{4}

Range:- Since $f(x)=\frac{-(x-4)}{x-4}=-1$

∴ Range is {−1}

Hence, the correct answer is option C.