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

Answer :

To find the formula for converting a temperature from degrees Fahrenheit to degrees Celsius, we need to find the inverse of the given function [tex]\( F(C) = \frac{9}{5} C + 32 \)[/tex].

Let's solve for the inverse step-by-step:

1. Start with the original equation:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]

2. Isolate the term with [tex]\( C \)[/tex]:
Subtract 32 from both sides:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]

3. Solve for [tex]\( C \)[/tex]:
Multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to get rid of the fraction:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]

This gives us the formula for converting from degrees Fahrenheit to degrees Celsius:
[tex]\[
C(F) = \frac{5}{9} F - \frac{5}{9} \times 32
\][/tex]

So, the coefficients in the answer boxes should be:

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

Therefore, the solution is:
[tex]\[ C(F) = \frac{5}{9} \times F - \frac{160}{9} \][/tex]

In this completion, the numerical value of [tex]\(\frac{5}{9} \times 32\)[/tex] was calculated to be [tex]\(\frac{160}{9}\)[/tex], which is the constant term in the Celsius conversion formula.

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