Question

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

Answer 1

`f" varies directly with "h.`

Explanation:

Given that, `f prop 1/g rArr f=m/g," where, "m ne0," a const."`

Similarly, `g prop 1/h rArr g=n/h," where, "n ne0," a const."`

`f=m/g rArr g=m/f,` and sub.ing in the `2^(nd)` eqn., we get,

`m/f=n/h rArr f=(m/n)h, or, f=kh, k=m/n ne 0,` a const.

`:. f prop h,`

`:. f" varies directly with "h.`