High School

The formula for converting a temperature in degrees Celsius to degrees Fahrenheit is given by:

[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 :

Given the Celsius to Fahrenheit conversion formula:

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

we want to find the inverse function, which converts a Fahrenheit temperature to Celsius. Here are the step-by-step details:

1. Start with the equation for Fahrenheit temperature:

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

2. Subtract 32 from both sides to isolate the term with [tex]$C$[/tex]:

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

3. Multiply both sides of the equation by the reciprocal of [tex]$\frac{9}{5}$[/tex], which is [tex]$\frac{5}{9}$[/tex], to solve for [tex]$C$[/tex]:

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

Thus, the formula for converting a temperature from Fahrenheit to Celsius is:

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

Here, note that the original conversion factor [tex]$\frac{9}{5}$[/tex] corresponds to approximately [tex]$1.8$[/tex], and its reciprocal [tex]$\frac{5}{9}$[/tex] is approximately [tex]$0.5556$[/tex]. The constant [tex]$32$[/tex] is subtracted before applying the inverse multiplier to complete the conversion.

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