High School

The formula for converting a temperature in degrees Celsius to degrees Fahrenheit is

\[ F(C) = \frac{9}{5} C + 32 \]

The inverse function will convert a temperature in degrees Fahrenheit to degrees Celsius. What is the formula for converting from degrees Fahrenheit to degrees Celsius?

\[ C(F) = \square F - \square \]

Answer :

Certainly! Let's find the formula to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).

We start with the formula for converting Celsius to Fahrenheit:
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]

To find the inverse function, which will convert Fahrenheit to Celsius, we need to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex]. Let's go through the steps:

1. Start with the given formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

2. Subtract 32 from both sides to isolate the term with [tex]\( C \)[/tex]:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]

3. Now, we need to get [tex]\( C \)[/tex] by itself. To do this, multiply both sides of the equation by [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

So, we have the formula for converting from degrees Fahrenheit to degrees Celsius:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

In the form given in the question:
[tex]\[ C(F) = \boxed{\frac{5}{9} F - \frac{160}{9}} \][/tex]

But we can also write it in the format:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]

This shows each operation clearly and simply.