### Home > PC > Chapter 5 > Lesson 5.1.1 > Problem5-5

5-5.

Suppose $f\left(x\right)$ varies directly as $\left(x^{2} − 4\right)$ and $f\left(3\right) = 2$. Find $f\left(4\right)$. Hint: First find $k$

Write the direct variation equation.

Substitute the given point to find k.

Write the function with the k value.

Find f(4).

$y=\frac{24}{5}$

$y = k\left(x^{2} − 4\right)$

$2 = k\left(3^{2} − 4\right)$
$2 = k\left(5\right)$

$k=\frac{2}{5}$

$y=\frac{2}{5}(x^2-4)$

$y=\frac{2}{5}(4^2-4)$

$y=\frac{2}{5}(12)$