Question #e8ec1

1 Answer
Oct 31, 2017

All real numbers ≥ 0.


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 :)