Answer
The inverse of the function $C\left( x \right)=\frac{100+5x}{x}$ is ${{C}^{-1}}\left( x \right)=\frac{100}{x-5}$, and it gives the number of people in the group, where $x$ is the cost per person in dollars.
Work Step by Step
$C\left( x \right)=\frac{100+5x}{x}$
Evaluate the inverse of the function $C\left( x \right)=\frac{100+5x}{x}$ as follows.
Replace the function $C\left( x \right)$ with y.
$y=\frac{100+5x}{x}$
Interchange the variables x and y.
$x=\frac{100+5y}{y}$
Solve for y value.
$\begin{align}
& x=\frac{100}{y}+5 \\
& x-5=\frac{100}{y} \\
& y=\frac{100}{x-5} \\
\end{align}$
Replace y with ${{C}^{-1}}\left( x \right)$ as follows.
${{C}^{-1}}\left( x \right)=\frac{100}{x-5}$
