The function varies inversely with x and when x = 16.f(x)f(x) = 2What is when x = 4?f(x)

when x = 4 then f(x) equals 8Explanation:The complete question is as follows: ___________________________________________The function f(x) varies inversely with x and f(x)=2 when x=16. What is f(x) when x=4? 128 72 40 8 ___________________________________________Inversely proportional means that if you held constant all other variables, then one variable decreases if the other variable increases. Hence [tex]y[/tex] varies inversely as [tex]x[/tex] or [tex]y[/tex] is inversely proportional to [tex]x[/tex] if and only if: [tex]y=\frac{k}{x} \\ \\ \ k \ is \ any \ non-zero \ constant \ and \ is \ called \ constant \ of \ proportionality[/tex]In this case:[tex]y=f(x) \\ \\ So: \\ \\ x=16 \\ \\ y=f(16)=2 \\ \\ k=yx \\ \\ k=(2)(16) \\ \\ k=32[/tex]So our expression is:[tex]y=\frac{32}{x}[/tex]We are asked to find f(x) when x=4, so:[tex]y=f(4)=\frac{32}{4} \\ \\ \boxed{y=f(4)=8}[/tex]In conclusion, when x = 4 then f(x) equals 8Learn more:Direct Proportion: