Paul's Online Notes
Home / Algebra / Graphing and Functions / The Definition of a Function
Show Mobile Notice Show All Notes Hide All Notes
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 views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll 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

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 $$w \ge - \frac{7}{9}$$.