Question

Find the domain and range of the function f(x) = (x² - 9)/(x - 3)

Answer 1

We have f(x) = (x² - 9)/(x - 3)

Domain off: Clearly f(x) is not defined for x – 3 = 0 

i.e. x = 3. 

Therefore, Domain (f) = R – {3} 

Range off: Let f(x) = y. Then,

f(x) = y 

(x² - 9)/(x - 3) = y 

x + 3 = y

It follows from the above relation that y takes all real values except 6 when x takes values in the set R – {3}. Therefore, Range (f) = R {6}.