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.
[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.