Answer :
To find the formula for converting a temperature from degrees Fahrenheit to degrees Celsius, we need to start with the given formula that converts Celsius to Fahrenheit:
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
Our goal is to find the inverse of this function, which will convert Fahrenheit back to Celsius. Here's how we can do it step by step:
1. Start with the given equation for Fahrenheit:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
2. Solve for Celsius (C):
- First, subtract 32 from both sides of the equation to isolate the term with C:
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
- Next, to eliminate the fraction, 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 we have the inverse function that allows us to convert degrees Fahrenheit to degrees Celsius:
[tex]\[ C(F) = \frac{5}{9} F - \left(\frac{5}{9} \times 32\right) \][/tex]
Simplifying the second part:
[tex]\[ \frac{5}{9} \times 32 \][/tex]
This results in subtracting 32 from F and multiplying the result by [tex]\(\frac{5}{9}\)[/tex].
Therefore, the completed formula for converting Fahrenheit to Celsius is:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
So, the formula using the placeholders provided in the question is:
[tex]\[ C(F) = \frac{5}{9} F - \frac{5}{9} \times 32 \][/tex]
This formula gives you the temperature in degrees Celsius when you start with a temperature in degrees Fahrenheit.
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
Our goal is to find the inverse of this function, which will convert Fahrenheit back to Celsius. Here's how we can do it step by step:
1. Start with the given equation for Fahrenheit:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
2. Solve for Celsius (C):
- First, subtract 32 from both sides of the equation to isolate the term with C:
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
- Next, to eliminate the fraction, 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 we have the inverse function that allows us to convert degrees Fahrenheit to degrees Celsius:
[tex]\[ C(F) = \frac{5}{9} F - \left(\frac{5}{9} \times 32\right) \][/tex]
Simplifying the second part:
[tex]\[ \frac{5}{9} \times 32 \][/tex]
This results in subtracting 32 from F and multiplying the result by [tex]\(\frac{5}{9}\)[/tex].
Therefore, the completed formula for converting Fahrenheit to Celsius is:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]
So, the formula using the placeholders provided in the question is:
[tex]\[ C(F) = \frac{5}{9} F - \frac{5}{9} \times 32 \][/tex]
This formula gives you the temperature in degrees Celsius when you start with a temperature in degrees Fahrenheit.