First slide

Introduction to real valued functions

Question

The domain of the function $f (x) = \sqrt{\frac{4 - x^{2}}{[x] + 2}}$ where [x] denotes the greatest integer less than or equal to x, is

Moderate

A

[-- 1, 2]
B

$(- \infty, - 2)$
C

$(- \infty, - 2) \cup [- 1, 2]$
D

none of these

Solution

For $f (x)$ to be real, we must have
$\frac{4 - x^{2}}{[x] + 2} > 0$ and $[x] + 2 \neq 0$
$\Rightarrow \frac{4 - x^{2}}{[x] + 2} > 0$ and $x \notin [- 2, - 1)$

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