Answer:
The inverse variation function can be written as:
[tex]f(x)=\frac{-200}{x}[/tex]
Step-by-step explanation:
Given :
[tex]f(x)[/tex] varies inversely with [tex]x[/tex]
when [tex]x=20[/tex], [tex]f(x)=-10[/tex]
To find the inverse variation equation.
Solution:
[tex]f(x)[/tex] varies inversely with [tex]x[/tex] can be represented as:
[tex]f(x)[/tex] ∝ [tex]\frac{1}{x}[/tex]
Thus, [tex]f(x)=\frac{k}{x}[/tex]
where [tex]k[/tex] represents the constant of proportionality.
We can determine the value of [tex]k[/tex] by plugging in the values given.
when [tex]x=20[/tex], [tex]f(x)=-10[/tex]
So, we have
[tex]-10=\frac{k}{20}[/tex]
Multiplying both sides by 20.
[tex]20\times (-10)=20\times \frac{k}{20}[/tex]
[tex]-200=k[/tex]
Thus the inverse variation function can be written as:
[tex]f(x)=\frac{-200}{x}[/tex]
