To find the temperature in degrees Celsius for a given temperature in degrees Fahrenheit, we need to determine the inverse of the function [tex]\( F(C) = \frac{9}{5}C + 32 \)[/tex]. Here’s the step-by-step process to find that inverse:
1. Start with the given formula:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
2. Isolate the term involving [tex]\(C\)[/tex]:
To do this, subtract 32 from both sides of the equation:
[tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
3. Solve for [tex]\(C\)[/tex]:
Next, we need to isolate [tex]\(C\)[/tex] by getting rid of the fraction [tex]\(\frac{9}{5}\)[/tex]. Multiply both sides of the equation by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
As a result, the formula to convert a temperature from Fahrenheit to Celsius is:
[tex]\[
C(F) = \frac{5}{9} (F - 32)
\][/tex]
This means if you have a temperature in degrees Fahrenheit, you can use this formula to find the equivalent temperature in degrees Celsius.
