Question

Write the domain and range of the function $f\left(x\right)=\frac{x-2}{2-x}$.

Answer 1

We have,
$f\left(x\right)=\frac{x-2}{2-x}$
Domain of f : Clearly, f(x) is defined for all $xϵR$ except for which
$2-x\ne 0i.e.,x\ne 2$
Hence, domain (f) = R - \{2\}
Range of f : Let f(x) = y
$\Rightarrow \frac{x-2}{2-x}=y\Rightarrow \frac{-1(2-x)}{2-x}=y\Rightarrow -1=y\Rightarrow y=-1$
$\therefore$ Range (f) = (-1).