# Question e8ec1

Oct 31, 2017

All real numbers ≥ 0.

#### Explanation:

Domain is simply the set of all possible values you can plug into a function.

When solving a domain problem, the best question you can ask is what values can I NOT plug into the function?

$f \left(x\right) = \sqrt{2 x} + 9 x - 2$

...the only possible problem you could have here is your square root: what is under the radical cannot be negative. Keeping this in mind:

2x ≥ 0
x ≥ 0#

As shown, the only values you cannot put into your function are values less than zero. Everything else is fine.

Hence, your domain would be all real numbers ≥ 0.

To get a visual sense of what this means, look at the graph of your function:

graph{sqrt(2x) + 9x - 2 [-35.86, 37.22, -12.4, 24.1]}

As you zoom in, you can see that the graph breaks at $x = 0$, and does not continue any further in the $- x$ direction. However, it does just fine in the $+ x$ direction, and will keep moving on till infinity.

Hope that helped :)