High School

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]$C(F) = \square F - \square$[/tex]

Answer :

Sure! Let's go through the steps to find the formula for converting temperature from degrees Fahrenheit to degrees Celsius.

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

2. We want to find the inverse formula:
- This inverse formula will allow us to convert from Fahrenheit back to Celsius.

3. Begin by setting the equation for Fahrenheit:
- Let [tex]\( F \)[/tex] be the temperature in Fahrenheit. We start with the equation [tex]\( F = \frac{9}{5} C + 32 \)[/tex].

4. Solve for [tex]\( C \)[/tex]:
- First, subtract 32 from both sides of the equation to isolate the term involving [tex]\( C \)[/tex]:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]

5. Remove the fraction by multiplying 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]

6. Conclude with the formula:
- So, the formula for converting a temperature from Fahrenheit to Celsius is:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]

This is the formula you can use to convert any temperature value from degrees Fahrenheit to degrees Celsius.

Other Questions