You did not answer: To convert from $x$ degrees Celsius to y degrees Fahrenheit, we use the formula $f(x)=\frac{9}{5} x+32$. Find the inverse function, if it exists, and be sure you could explain its meaning. \[ f^{-1}(x)= \] help (formulas)

Step 1 ：The problem is asking for the inverse function of the given function, which is used to convert Celsius to Fahrenheit. The inverse function, if it exists, would convert Fahrenheit to Celsius. To find the inverse function, we need to swap x and y in the original equation and solve for y.

Step 2 ：Starting with the original equation \(f(x) = \frac{9}{5}x + 32\), we swap x and y to get \(x = \frac{9}{5}y + 32\).

Step 3 ：Solving for y, we get the inverse function \(f^{-1}(x) = \frac{5}{9}(x - 32)\).

Step 4 ：This function can be approximated as \(f^{-1}(x) = 0.555555555555556x - 17.7777777777778\).

Step 5 ：\(\boxed{f^{-1}(x) = \frac{5}{9}(x - 32)}\) is the final answer. This function converts Fahrenheit to Celsius.