Discuss the continuity of the function f(x) = at x = 1

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 11, 2026

Discuss the continuity of the function

f(x) = at x = 1

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

Sol. f(1) = = (log3 – sin1)

 x 2n =

Therefore, for x 2 < 1 f(x) = =

log (2 + x) and for x 2 > 1,

f(x) = = – sin x

∴ f(x) =

∴ f(x) = log (2 + x) = log 3

and f(x) = – sin x = – sin 1

⇒ f(x) ≠ f(x)

∴ f(x) is discontinuous at x = 1

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