Find the domain and range of the following real functions f(x)=x^2-9/x-3

Question

Find the domain and range of the following real functions

f(x)=\(\frac{x^2-9}{x-3}\)

Answer 1

Given, f(x) =\(\frac{x^2-9}{x-3}\) 

Domain: Clearly, f(x) is defined for all x ∈ R expect x = 3 

∴ Domain of f = R – {3} = (−∞, 3),∪ (3, ∞) 

Range: Let y = f(x) 

∴ y = \(\frac{x^2-9}{x-3}\)⇒ = + 3 

It follow from the above relation that y takes all real values except 6 when takes values in the set 

R – {3} 

∴ Range of f = R – {6}