Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Discuss the continuity of the function f(x) given by
f(x) = 
at x = 1.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. For 0 < x < 1, we have
f(x) = 
= 
= cos π x
At x = 1, we have f(x) = 
= 
= –1 For x > 1, we have
f(x) = 
= 
= 
= – 
Thus f(x) = 
Now 
f(x) = 
cos π x = –1
and 
f(x) = 
– 
= –1
Also f(1) = –1
∴ 
f(x) = 
f(x) = f(1) = –1
Hence f(x) is continuous at x = 1.
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