# If f(x) = x^3 - 15/x, what is f(-1/3)?

Jan 29, 2016

$f \left(- \frac{1}{3}\right) = \frac{1214}{27}$

#### Explanation:

To compute $f \left(- \frac{1}{3}\right)$, you need to plug $- \frac{1}{3}$ for every occurence of $x$ in your $f \left(x\right)$ term:

$f \left(\textcolor{b l u e}{x}\right) = {\textcolor{b l u e}{x}}^{3} - \frac{15}{\textcolor{b l u e}{x}}$

Replace each $\textcolor{b l u e}{x}$ with $\textcolor{p u r p \le}{- \frac{1}{3}}$:

$f \left(\textcolor{p u r p \le}{- \frac{1}{3}}\right) = {\left(\textcolor{p u r p \le}{- \frac{1}{3}}\right)}^{3} - \frac{15}{\textcolor{p u r p \le}{- \frac{1}{3}}}$

$= - {1}^{3} / {3}^{3} + \frac{15}{\frac{1}{3}}$

... to resolve the double fraction, remember that dividing by $\frac{1}{3}$ is the same thing as multiplying with the reciprocal, namely $\frac{3}{1} = 3$...

$= - \frac{1}{3} ^ 3 + 15 \cdot 3$

$= - \frac{1}{27} + 45$

$= \textcolor{w h i t e}{x} 44 \frac{26}{27} = \frac{1214}{27}$,

whichever formulation you prefer.

Hope that this helped!