Find the domain and range of the following real functionsf(x)=\(\frac{

1.	Find the domain and range of the following real functionsf(x)=\(\frac{x^2-9}{x-3}\)
Answer» 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}

Find the domain and range of the following real functionsf(x)=\(\frac{x^2-9}{x-3}\)

Answer»

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}