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### Section 1-1 : Review : Functions

23. Find the domain of $$\displaystyle f\left( w \right) = \frac{{{w^3} - 3w + 1}}{{12w - 7}}$$.

Show Solution

In this case we need to avoid division by zero issues so we’ll need to determine where the denominator is zero. To do this we will solve,

$12w - 7 = 0\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}w = \frac{7}{{12}}$

We can plug all other values of $$w$$ into the function without any problems and so the domain is,

${\mbox{Domain : All real numbers except }}w = \frac{7}{{12}}$