The range of the function f x = sin ⁡ π x + 1 x 4 + 1 (where, · is the greatest integer function) is

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The range of the function

f (x) = \frac{\sin (π [x + 1])}{x^{4} + 1}

(where,

[\cdot]

is the greatest integer function) is

MathematicsFunctionsJEE Main

Options:

A $[0, 1]$
B $[- 1, 1]$
C $\{0\}$
D None of these

Solution:

1588 Upvotes Verified Answer

The correct answer is:

\{0\}

Since,

[x + 1]

is an integer

∴ f (x) = \frac{\sin (π [x + 1])}{x^{4} + 1} = 0

Hence, range of

f = R_{f} = \{0\}

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