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If f(x) = cos x + (sin (where (.] denotes the greatest integer function), then f(x) is (A) even (C) even and odd simultaneously (B) odd (D) none of these

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Similar Questions

Q1

If

f (x) = \frac{cos x}{[\frac{x}{π}] + \frac{1}{2}},

where

x

is not an integral multiple of

π

and

[.]

denotes the greatest integer function, then

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Q2

If

f (x)

is an odd function then-
(i)

\frac{f (- x) + f (x)}{2}

is an even function
(ii)

[∣ f (x) ∣ + 1]

is even where [.] denotes greatest integer function.
(iii)

\frac{f (x) - f (- x)}{2}

is neither even nor odd
(iv)

f (x) + f (- x)

is neither even nor odd
Which of these statements are correct

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Q3

The function $f (x) = (t a n x^{11}) e^{x^{5}} s g n (x^{11}) [\frac{1}{3 x^{2} + 2}]$ where $[\cdot]$ denotes greatest integer function, is:

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Q4

Determine whether function;

f (x) = (- 1)^{[x]}

is even, odd or neither of the two (where

[\cdot]

denotes the greatest integer function).

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Q5

Find whether the given function is even or odd function, where

f (x) = \frac{x (sin x + tan x)}{[\frac{x + π}{π}] - \frac{1}{2}}

, where

x \neq n π

, where

[]

denotes the greatest integer function.

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