Question

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

Answer 1

f(x) = $\frac{4-x}{x-4}$
Domain :- for f(x) = $\frac{4-x}{x-4}$
x − 4$\ne$0
i.e x$\ne$4
∴ Domain is R −{4}
Range:- Since f(x) = $\frac{-\left(x-4\right)}{x-4}=-1$
∴ Range is {−1}
Hence, the correct answer is option C.