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}.