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

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Answer 1 · 2016-01-29T19:43:47

$f(-1/3) = 1214/27$

To compute $f(- 1/3)$ , you need to plug $-1/3$ for every occurence of $x$ in your $f(x)$ term:

$f(color(blue)(x)) = color(blue)(x)^3 - 15 / color(blue)(x)$

Replace each $color(blue)(x)$ with $color(purple)(-1/3)$ :

$f(color(purple)(-1/3)) = (color(purple)(-1/3))^3 - 15 / (color(purple)(-1/3))$

$= - 1^3 / 3^3 + 15 / (1/3)$

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

$= - 1 / 3^3 + 15 * 3$

$= - 1 / 27 + 45$

$= color(white)(x) 44 26/27 = 1214/27$ ,

whichever formulation you prefer.

Hope that this helped!

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