Answer :
To convert a temperature from degrees Fahrenheit to degrees Celsius, we need to find the inverse function of the given formula [tex]\( F(C) = \frac{9}{5}C + 32 \)[/tex].
Here's how you can derive the formula step-by-step:
1. Start with the original formula for Fahrenheit:
[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, multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to solve for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
This formula, [tex]\( C = \frac{5}{9}(F - 32) \)[/tex], is used to convert a temperature in degrees Fahrenheit to degrees Celsius.
Here's how you can derive the formula step-by-step:
1. Start with the original formula for Fahrenheit:
[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, multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to solve for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
This formula, [tex]\( C = \frac{5}{9}(F - 32) \)[/tex], is used to convert a temperature in degrees Fahrenheit to degrees Celsius.
