Question

Examine the continuity of f(x) = `(x^2 - 9)/(x - 3)` on R.

Answer 1

f(x) = `(x^2 - 9)/(x - 3)`; x ∈ R

f(x) is a rational function and is continuous for all x ∈ R, except at the points where denominator becomes zero. Here, denominator x – 3 = 0 when x = 3.
∴ Function f is continuous for all x ∈ R, except at x = 3, where it is not defined.