Question

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

Answer 1

Given:
$f\left(x\right)=\frac{x-2}{2-x}$
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
⇒ $\frac{x-2}{2-x}=y$
⇒ x $-$ 2 = y (2 $-$ x)
⇒ x $-$ 2 = $-$ y (x $-$ 2)
⇒ y = $-$ 1
Hence, range ( f ) = {$-$ 1}.