find the domain and range

Question

find the domain and range of x²-4/x-2

Answer 1

f(x) = (x² - 4)/(x-2)

 

The only restriction on the domain is x≠2 since we cannot divide by zero.

Domain = (-∞, 2) U (2,∞)

 

Range:

f(x) = (x²-4)/(x-2) = [(x-2)(x+2)]/(x-2) = x+2

The output of this is all real numbers except for f(x) = 4

because x ≠2

Range:  (- ∞, 4) U (4, ∞)