# What is the domain and range of Q(s)=1/(sqrt(2s))?

Jun 27, 2018

Domain: $\left(0 , + \infty\right)$ Range: $\left(0 , + \infty\right)$

#### Explanation:

$Q \left(s\right) = \frac{1}{\sqrt{2 s}}$

$Q \left(s\right)$ is defined for $\sqrt{2 s} \ne 0$

Assuming $Q \left(s\right) \in \mathbb{R} \to 2 s \ge 0$

Thus $s > 0$

$\therefore$ the domain of $Q \left(s\right)$ is $\left(0 , + \infty\right)$

Consider:

${\lim}_{s \to + \infty} Q \left(s\right) = 0 \mathmr{and} {\lim}_{s \to 0} Q \left(s\right) \to + \infty$

$\therefore$ the range of $Q \left(s\right)$ is also $\left(0 , + \infty\right)$

We can deduce these results from the graph of $Q \left(s\right)$ below.

graph{1/sqrt(2x) [-3.53, 8.96, -2.18, 4.064]}