Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f(x) = 
and g(x) = x(1 –x 2 ), then discuss the continuity of f(g(x)) and g(f(x)).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. The signs of g(x) for different values of x are
⇒ f(g(x)) = 
⇒ f(g(x)) = 
And g(f(x)) = 
⇒ g (f(x)) = 
∴ g(f(x)) = 0 ∀ x ∈ R
Now f (g(x)) is discontinuous at x = –1, 0 , 1 and since g(f(x)) is a constant function, therefore g(f(x)) is continuous everywhere.
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