Given the function f(x) = Find the point of discontinuity of the composite function y = (f(x)).

Question

Philoid · Accepted Answer

Given,

f(x) =

To find: Points discontinuity of composite function f(f(x))

As f(x) is not defined at x = -2 as denominator becomes 0,at x = -2.

∴ x = -2 is a point of discontinuity

∵ f(f(x)) =

Clearly f(f(x)) is not defined at x = -5/2 as denominator becomes 0, at x = -5/2.

∴ x = -5/2 is another point of discontinuity

Thus f(f(x)) has 2 points of discontinuity at x = -2 and x = -5/2