Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Discuss the continuity and differentiability of the function f(x) = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
At x = 0 differentiable and at x = ±1 discontinuous
Sol. f(x) = 
f(x) = 
= 0 and 
f(x) = 
= 0
and f (0) = 0 ∴ f(x) is continuous at x = 0
f(x) = 
= 
and 
f(x) = 
→ ∞
∴ f(x) is discontinuous for x = 1
Similarly we can check that f(x) is discontinuous at x = – 1
L.H.D. at (x = 0) is = 
= 
= 1
R.H.D. at (x = 0) is = 
= 
= 1
⇒ L.H.D. = R.H.D.
∴ at x = 0, f(x) is derivable.
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