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. (If an answer does not exist, enter DNE.) $$ f^{-1}(x)= $$ Explain its meaning. The inverse formula allows you to convert from $$ x $$ degrees Celsius to $$ y $$ degrees Fahrenheit. The inverse formula allows you to convert from $$ x $$ degrees Fahrenheit to $$ y $$ degrees Celsius. There is no inverse function.

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Let $$ y = f(x) $$, so

$$
y = \frac{9}{5}x + 32.
$$

To find the inverse, we solve for $$ x $$:

1. Subtract 32 from both sides:

$$
y - 32 = \frac{9}{5}x.
$$

2. Multiply both sides by $$ \frac{5}{9} $$ to isolate $$ x $$:

$$
x = \frac{5}{9}(y - 32).
$$

Now, swap $$ x $$ and $$ y $$ to write the inverse function:

$$
f^{-1}(x) = \frac{5}{9}(x - 32).
$$

This inverse function converts a temperature in Fahrenheit to the equivalent temperature in Celsius.
The inverse function is $$ f^{-1}(x) = \frac{5}{9}(x - 32) $$. This allows you to convert a temperature from Fahrenheit to Celsius.

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