# Suppose f varies inversely with g and g varies inversely with h, what is the relationship between f and h?

Jun 12, 2017

$f \text{ varies directly with } h .$

#### Explanation:

Given that, $f \propto \frac{1}{g} \Rightarrow f = \frac{m}{g} , \text{ where, "m ne0," a const.}$

Similarly, $g \propto \frac{1}{h} \Rightarrow g = \frac{n}{h} , \text{ where, "n ne0," a const.}$

$f = \frac{m}{g} \Rightarrow g = \frac{m}{f} ,$ and sub.ing in the ${2}^{n d}$ eqn., we get,

$\frac{m}{f} = \frac{n}{h} \Rightarrow f = \left(\frac{m}{n}\right) h , \mathmr{and} , f = k h , k = \frac{m}{n} \ne 0 ,$ a const.

$\therefore f \propto h ,$

$\therefore f \text{ varies directly with } h .$