# Find the domain of f?

## Let f be given by the formula:

Mar 1, 2018

$\left(- \infty , - 3\right) \cup \left(1 , \infty\right)$

#### Explanation:

The domain is defined as all possible values of $x$ for which $f \left(x\right)$ will be defined.

Here, as ${x}^{2} + 2 x - 3 \rightarrow 0$, $f \left(x\right) \rightarrow \pm \infty$ .

We can say that $f \left(x\right)$ is undefined when ${x}^{2} + 2 x - 3 = 0$. Solving for $x$:

${x}^{2} + 2 x - 3 = 0$

${x}^{2} + 3 x - x - 3 = 0$

$x \left(x + 3\right) - 1 \left(x + 3\right) = 0$

$\left(x + 3\right) \left(x - 1\right) = 0$

So $f \left(x\right)$ is undefined when $x = 1$ and $x = - 3$.

In interval notation, we can write this as:

$\left(- \infty , - 3\right) \cup \left(1 , \infty\right)$