Answer :
To find the inverse of the function that converts degrees Celsius (C) to degrees Fahrenheit (F), we need to rearrange the formula to solve for C in terms of F. The original formula is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
To find the inverse, follow these steps:
1. Start with the original equation:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Isolate the term involving C:
Subtract 32 from both sides:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. 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]
Therefore, the formula for converting a temperature from degrees Fahrenheit to degrees Celsius is:
[tex]\[ C(F) = \frac{5}{9}F - \frac{5}{9} \times 32 \][/tex]
Simplifying the constant term:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This is the formula you can use to convert temperatures from Fahrenheit to Celsius!
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
To find the inverse, follow these steps:
1. Start with the original equation:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Isolate the term involving C:
Subtract 32 from both sides:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. 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]
Therefore, the formula for converting a temperature from degrees Fahrenheit to degrees Celsius is:
[tex]\[ C(F) = \frac{5}{9}F - \frac{5}{9} \times 32 \][/tex]
Simplifying the constant term:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This is the formula you can use to convert temperatures from Fahrenheit to Celsius!