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

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

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Answer 1 · 2017-06-12T17:39:17

$f varies directly with h .$ $f" varies directly with "h.$

Explanation:

Given that, $f \propto \frac{1}{g} \Rightarrow f = \frac{m}{g}, where, m \neq 0, a const.$ $f prop 1/g rArr f=m/g," where, "m ne0," a const."$

Similarly, $g \propto \frac{1}{h} \Rightarrow g = \frac{n}{h}, where, n \neq 0, a const.$ $g prop 1/h rArr g=n/h," where, "n ne0," a const."$

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

$\frac{m}{f} = \frac{n}{h} \Rightarrow f = (\frac{m}{n}) h, or, f = k h, k = \frac{m}{n} \neq 0,$ $m/f=n/h rArr f=(m/n)h, or, f=kh, k=m/n ne 0,$ a const.

$:. f prop h,$

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

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

1 Answer

Explanation:

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