Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the points of discontinuity of the composite function f{f (f(x))} if f(x) = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. f(x) is not defined at x = 1, also, it is a point of discontinuity of f(x).
If x ≠ 1, then
g(x) = fof(x) = f(f(x)) = f 
= 
= 
⇒ g(x) is discontinuous at x = 0
∴ g(x) is discontinuous at x = 0, 1
If x ≠ 0, 1 then h(x) = f {f(f(x))} = f 
= 
= x which is continuous everywhere. Thus h(x) is discontinuous at x = 0, 1.
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