Answer :
To find the formula for converting a temperature from degrees Fahrenheit to degrees Celsius, we'll start by looking at the original formula given for converting Celsius to Fahrenheit:
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
We need to find the inverse of this function, which will give us a formula for converting Fahrenheit back to Celsius.
Step 1: Write the Formula for Fahrenheit
The formula to convert Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
Step 2: Solve for C (Celsius)
To find the inverse function, we need to solve this equation for [tex]\( C \)[/tex].
1. Subtract 32 from both sides of the equation:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
2. Multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to isolate [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9} \times (F - 32)
\][/tex]
Now, we have the inverse function that converts Fahrenheit to Celsius:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
This is the formula you can use to convert a temperature in degrees Fahrenheit to degrees Celsius.
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
We need to find the inverse of this function, which will give us a formula for converting Fahrenheit back to Celsius.
Step 1: Write the Formula for Fahrenheit
The formula to convert Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
Step 2: Solve for C (Celsius)
To find the inverse function, we need to solve this equation for [tex]\( C \)[/tex].
1. Subtract 32 from both sides of the equation:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
2. Multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to isolate [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9} \times (F - 32)
\][/tex]
Now, we have the inverse function that converts Fahrenheit to Celsius:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
This is the formula you can use to convert a temperature in degrees Fahrenheit to degrees Celsius.
