First slide

Functions (XII)

Question

If $f (x) = \frac{\sin ([x] π)}{x^{2} + x + 1}$ where [.] denotes the greatest integer function, then

Moderate

A

f is one-one
B

f is not one-one and non-constant
C

f is a constant function
D

none of these

Solution

$\begin{array}{l} f (x) = \frac{\sin [x] π}{x^{2} + x + 1} \\ Let [x] = n ≃ integer \\ ∴ \sin [x] π = 0 \\ or f (x) = 0 \\ Hence, f (x) is constant function . \end{array}$

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