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.
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