College

Finding the Inverse of a Function

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

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

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?

[tex]C(F) = \frac{5}{9}(F - \square)[/tex]

Answer :

To find the formula for converting from degrees Fahrenheit to degrees Celsius, we'll need to find the inverse of the function that converts Celsius to Fahrenheit.

1. Start with the given function:
The formula that converts Celsius (C) to Fahrenheit (F) is:
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]

2. Set the equation for Fahrenheit:
We have [tex]\( F = \frac{9}{5}C + 32 \)[/tex]. To find the inverse, we need to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex].

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

4. Solve for [tex]\( C \)[/tex]:
To isolate [tex]\( C \)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

5. Conclusion:
The formula for converting from degrees Fahrenheit to degrees Celsius is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

This formula will allow you to convert any temperature from degrees Fahrenheit to degrees Celsius.