Prove that f(x) = is an odd function, where [.] denotes th…

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 11, 2026

Prove that f(x) = is an odd function, where [.] denotes the greatest integer function.

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

Sol.  f(x) =

⇒ f(x) =

⇒ f(–x) =

Now,

Case I ; when is an integer i.e. x = n π (say);

n ∈ I ; = –

and x (sin x + tan x) = 2 π (sin n π + tan n π ) = 0

⇒ f(– x) = 0 ∀ x

⇒ f(x) = 0 ∀ x

Case- II -

when is not an integer; = – –1

∴ f(–x) = = –f(x)

Thus f(–x) = –f(x) in both cases. Hence f(x) is an odd function.

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