First slide

Functions (XII)

Question

The domain of the function $f (x) = \frac{\sin x}{\sqrt{|x| - x}}$ is

Moderate

A

$R$
B

$R ~ {0}$
C

$R^{+}$
D

$R^{-}$

Solution

For f(x) to be defined, we have $|x| > x .$ Since $|x| \geq x \forall x \in R$ and $|x| = x$ for $x \in [0, \infty)$ so $|x| > x$ if $x \in R = (- \infty, 0)$

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