# How do you find the domain and range of g(x) = 9x + 5?

Oct 9, 2017

$x \in \mathbb{R}$ and $g \left(x\right) \in \mathbb{R}$ or $x \in \left(- \infty , + \infty\right)$ and $g \left(x\right) \in \left(- \infty , + \infty\right)$

#### Explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

So, here we can let $x$ be any real number and our output will be a real number.

The real values of $y$ (in this case $g \left(x\right)$) is called the range.

Here too, the range can be any real number.

For example-->

Let $x = \sqrt{2}$ (which is a real number)

Then $g \left(x\right) = 9 \sqrt{2} + 5$ (which is also a real number)

So for all real values of $x$ we get real values of $g \left(x\right)$

Therefore, $x \in \left(- \infty , + \infty\right)$ and $g \left(x\right) \in \left(- \infty , + \infty\right)$