# How do you find the domain of g(t)=(t+4)/(t^2-16)?

Oct 10, 2017

$t \ne \pm 4$ or $t \in \left(- \infty , + \infty\right) - \left\{\pm 4\right\}$ or $t \in \mathbb{R} - \left\{\pm 4\right\}$

#### Explanation:

The function is g(x)=(t+4)/(t^2-16

Its written in the form of a fraction. As we know the denominator of a fraction can never be $0$, therefore we'll apply a condition to the function.

${t}^{2} - 16 \ne 0$

${t}^{2} \ne 16$

$t \ne \sqrt{16}$

Therefore

$t \ne \pm 4$

So $t$ can be any number except $\pm 4$

If you want to write it in interval notation it can be written as:-

$t \in \left(- \infty , + \infty\right) - \left\{\pm 4\right\}$

$$             or


$t \in \mathbb{R} - \left\{\pm 4\right\}$