Answer :
To find the formula for converting from degrees Fahrenheit to degrees Celsius, we need to find the inverse of the given function [tex]\( F(C) = \frac{9}{5} C + 32 \)[/tex]. The inverse function, [tex]\( C(F) \)[/tex], will express Celsius in terms of Fahrenheit.
Here’s how to find the inverse:
1. Start with the original formula:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
2. Solve for [tex]\( C \)[/tex]:
- First, subtract 32 from both sides to isolate the term with [tex]\( C \)[/tex]:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
- Next, to solve for [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]
Now, you have the inverse function, which converts Fahrenheit to Celsius:
[tex]\[
C(F) = \frac{5}{9} (F - 32)
\][/tex]
This formula tells you that to convert a temperature from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then multiply the result by [tex]\(\frac{5}{9}\)[/tex].
Here’s how to find the inverse:
1. Start with the original formula:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
2. Solve for [tex]\( C \)[/tex]:
- First, subtract 32 from both sides to isolate the term with [tex]\( C \)[/tex]:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
- Next, to solve for [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]
Now, you have the inverse function, which converts Fahrenheit to Celsius:
[tex]\[
C(F) = \frac{5}{9} (F - 32)
\][/tex]
This formula tells you that to convert a temperature from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then multiply the result by [tex]\(\frac{5}{9}\)[/tex].
