Write the domain and range of the function f(x)

Given:

$f(x)=\frac{x-2}{2-x}$

Domain ( f ) :

Clearly,  f (x) is defined for all x satisfying: if 2 -">−-x  ≠ 0 ⇒ x ≠ 2.

Hence, domain ( f ) = R -">−- {2}

Range of f :

Let f (x) = y

$\Rightarrow \frac{x-2}{2-x}=y$

$\Rightarrow x-2=y(2-x)$

$\Rightarrow x-2=-y(x-2)$

$\Rightarrow y=-1$

Hence, range $(f)=\{-1\} .$