Answer :
To find the inverse function that will convert a temperature from degrees Fahrenheit to degrees Celsius, we need to start with the given formula for converting Celsius to Fahrenheit:
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]
We want to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex], which means we need to find the inverse of this function. Here’s how to do it step by step:
1. Start with the equation:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Isolate [tex]\( C \)[/tex]:
- First, subtract 32 from both sides to remove the constant term added to [tex]\( C \)[/tex]:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. Solve for [tex]\( C \)[/tex]:
- To get [tex]\( C \)[/tex] by itself, multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
This gives us the formula for converting from Fahrenheit to Celsius:
[tex]\[ C(F) = (F - 32) \times \frac{5}{9} \][/tex]
So, to convert a temperature from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, and then multiply the result by [tex]\(\frac{5}{9}\)[/tex].
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]
We want to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex], which means we need to find the inverse of this function. Here’s how to do it step by step:
1. Start with the equation:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Isolate [tex]\( C \)[/tex]:
- First, subtract 32 from both sides to remove the constant term added to [tex]\( C \)[/tex]:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. Solve for [tex]\( C \)[/tex]:
- To get [tex]\( C \)[/tex] by itself, multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
This gives us the formula for converting from Fahrenheit to Celsius:
[tex]\[ C(F) = (F - 32) \times \frac{5}{9} \][/tex]
So, to convert a temperature from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, and then multiply the result by [tex]\(\frac{5}{9}\)[/tex].