Question

Question #e8ec1

Answer 1

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?

For your function:
`f(x) = sqrt(2x) + 9x - 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 :)