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 :

We start with the conversion formula:

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

We want to convert from degrees Fahrenheit to degrees Celsius, so we need the inverse function. To do this, let [tex]$F$[/tex] be a temperature in Fahrenheit and [tex]$C$[/tex] be the corresponding temperature in Celsius. Write the equation in terms of [tex]$C$[/tex]:

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

Step 1: Subtract 32 from both sides.

Subtracting 32 gives

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

Step 2: Multiply both sides by [tex]$\frac{5}{9}$[/tex].

Multiplying by [tex]$\frac{5}{9}$[/tex] to solve for [tex]$C$[/tex], we have

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

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

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

This is the final result.