Question

The function f(x) varies inversely with x and f(x) =6 when x =4 what time s f(x) when x = 8

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \textit{we also know that } \begin{cases} \stackrel{f(x)}{y}=6\\ ~~ x=4 \end{cases}\implies 6=\cfrac{k}{4}\implies 24=k~\hfill \boxed{y=\cfrac{24}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad \qquad y=\cfrac{24}{8}\implies y=3$