Algebra - The Definition of a Function

Show General Notice Show Mobile Notice Show All Notes Hide All Notes

General Notice

I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.

Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.

Paul
February 18, 2026

Mobile Notice

You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 3.4 : The Definition of a Function

Back to Problem List

17. Determine the domain of the following function.

\[g\left( w \right) = \sqrt {9w + 7} \] Show Solution

Recall that the domain is simply all the values of \(w\) that we can plug into the function and the resulting function value will be a real number.

In this case we have a square root and so we know that we need to require that the quantity under the root be positive or zero.

In other words, we need to require,

\[\begin{align*}9w + 7 & \ge 0\\ 9w & \ge - 7\\ w & \ge - \frac{7}{9}\end{align*}\]

Therefore, the domain for this function is \(w \ge - \frac{7}{9}\).