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]

To convert a temperature from degrees Fahrenheit to degrees Celsius, we need to find the inverse of the given function:

1. Start with the given formula for Celsius to Fahrenheit:

[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]

2. We want to express C in terms of F. Start by rearranging the equation:

[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

3. Subtract 32 from both sides to isolate the term with C:

[tex]\[ F - 32 = \frac{9}{5}C \][/tex]

4. To solve for C, 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]

5. Distribute the [tex]$\frac{5}{9}$[/tex] across [tex]$F - 32$[/tex]:

[tex]\[ C = \frac{5}{9}F - \frac{5}{9} \times 32 \][/tex]

6. Calculate [tex]$\frac{5}{9} \times 32$[/tex]:

[tex]\[\frac{5}{9} \times 32 = 17.77777777777778\][/tex]

Thus, the formula to convert degrees Fahrenheit to degrees Celsius is:

[tex]\[ C(F) = 0.5555555555555556F - 17.77777777777778 \][/tex]

So, to convert from Fahrenheit to Celsius, you multiply the Fahrenheit temperature by approximately 0.5556 and then subtract approximately 17.78.