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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 \(w \ge - \frac{7}{9}\).