# If f(x) varies directly with x and f(x) = 24 when x = –4, then what is f(x) when x = 12?

$f \left(12\right) = - 72$

#### Explanation:

Given that $f \left(x\right)$ varies directly with $x$ hence let

$f \left(x\right) = k x$

Where $k$ is some arbitrary constant

Now, given that $f \left(- 4\right) = 24$ hence

$k \left(- 4\right) = 24$

$k = - 6$

$\setminus \implies f \left(x\right) = - 6 x$

$\setminus \therefore f \left(12\right) = - 6 \left(12\right)$

$= - 72$