First slide

Functions (XII)

Question

Let $f : [- 10, 10] \to R,$ where $f (x) = \sin x + [\frac{x^{2}}{a}]$ , be an odd function. Then the set of values of parameter a is/are

Moderate

A

$(- 10, 10) ~ \{0\}$
B

$(0, 10)$
C

$[100, \infty)$
D

$(100, \infty)$

Solution

Since f(x) is an odd function,
$\begin{array}{l} [\frac{x^{2}}{a}] = 0 for all x \in [- 10, 10] \\ or 0 \leq \frac{x^{2}}{a} < 1 for all x \in [- 10, 10] or a > 100 \end{array}$

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