# How do you find f(20), if f(x) varies inversely with x and f(12)=5?

May 10, 2018

$f \left(20\right) = 3$

#### Explanation:

As $f \left(x\right)$ varies inversely as $x$, we have $f \left(x\right) = k \cdot \frac{1}{x}$

and as $f \left(12\right) = 5$, we have $k \cdot \frac{1}{12} = 5$ i.e. $k = 12 \times 5 = 60$

Hence $f \left(x\right) = 60 \cdot \frac{1}{x} = \frac{60}{x}$

and $f \left(20\right) = \frac{60}{20} = 3$