Question

Find the domain and range of the real valued function:

(v) \[f\left( x \right) = \frac{x - 2}{2 - x}\]

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}.