Question

Given the function f(x) = `1/(x + 2)`. Find the points of discontinuity of the composite function y = f(f(x))

Answer 1

f(x) = `1/(x + 2)`

f[f(x)] = `1/("f"(x) + 2)`

= `1/(1/(x + 2) + 2)`

= `1/((1 + 2x + 4)/(x + 2))`

= `(x + 2)/(2x + 5)`

∴ f[f(x)] = `(x + 2)/(2x + 5)`

This function will not be defined and continuous where 2x + 5 = 0

⇒ x = `(-5)/2`.

Hence, x = `(-5)/2` is the point of discontinuity.