Math Snap

STEP 1

Assumptions1. The function f(x) = \frac{9}{5}x +32 converts temperatures from Celsius to Fahrenheit.
. We are asked to find the inverse of this function, which will convert temperatures from Fahrenheit to Celsius.

STEP 2

First, let's write down the function we are given.
$$f(x) = \frac{9}{5}x +32$$

STEP 3

To find the inverse of a function, we first replace the function notation f(x) with y. This gives us$$y = \frac{9}{5}x +32$$

STEP 4

The next step in finding the inverse of a function is to swap x and y. This gives us$$x = \frac{9}{}y +32$$

STEP 5

Now, we need to solve this equation for y to get the inverse function. First, we subtract32 from both sides$$x -32 = \frac{9}{5}y$$

STEP 6

Next, we multiply both sides by \frac{5}{9} to isolate y$$y = \frac{5}{9}(x -32)$$

This is the inverse function, which we can write as$$f^{-1}(x) = \frac{5}{9}(x -32)$$So, the inverse of the function f(x) = \frac{9}{5}x +32 is f^{-1}(x) = \frac{5}{9}(x -32). This function converts temperatures from Fahrenheit to Celsius.