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.
[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.