Question

Which of the following functions f has removable discontinuity at x = x ? If the discontinuity is removable, find a function g that agrees with f for x ≠ x and is continuous on R.

(i) \(f(x) = \frac{x^2-2x-8}{x+2}\), x₀ = -2

(ii) \(f(x) =\frac{x^3+64}{x+4}\), x₀ = -4

(iii) \(f(x)=\frac{3-\sqrt{x}}{9-x}\), x₀ = 9

Answer 1

(i) \(f(x) = \frac{x^2-2x-8}{x+2}\)

(ii) \(f(x) =\frac{x^3+64}{x+4}\)

(iii) \(f(x)=\frac{3-\sqrt{x}}{9-x}\), has a removable discontinuity at x = 9