The range of the function fx=(sin⁡πx+1)/(x^4+1) (where, · is the greatest integer function) is

Correct answer: (C) 0. Since, x+1 is an integer ∴fx=(sin⁡πx+1)/(x^4+1)=0 Hence, range of f=R_f=0

Q24 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

The range of the function $f (x) = \frac{\sin (π [x + 1])}{x^{4} + 1}$ (where, $[\cdot]$ is the greatest integer function) is

Since,

[x + 1]

is an integer

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

Hence, range of

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

Hence, the correct answer is option: 'C'.