Answer :
Sure! Let's find the inverse of the function [tex]\( F(C) = \frac{9}{5} C + 32 \)[/tex], which converts a temperature from Celsius to Fahrenheit.
To find the inverse, we need to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex]. Here's how we can do it step by step:
1. Start with the original function:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
2. Isolate the term with [tex]\( C \)[/tex]:
To do this, subtract 32 from both sides:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
3. Solve for [tex]\( C \)[/tex]:
Now, to get [tex]\( C \)[/tex] by itself, multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
Now we have expressed [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex], which is the inverse function. Therefore, the inverse function is:
[tex]\[
C(F) = \frac{5}{9} (F - 32)
\][/tex]
This function [tex]\( C(F) \)[/tex] will convert a temperature from Fahrenheit back to Celsius.
To find the inverse, we need to solve for [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex]. Here's how we can do it step by step:
1. Start with the original function:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
2. Isolate the term with [tex]\( C \)[/tex]:
To do this, subtract 32 from both sides:
[tex]\[
F - 32 = \frac{9}{5} C
\][/tex]
3. Solve for [tex]\( C \)[/tex]:
Now, to get [tex]\( C \)[/tex] by itself, multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
Now we have expressed [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex], which is the inverse function. Therefore, the inverse function is:
[tex]\[
C(F) = \frac{5}{9} (F - 32)
\][/tex]
This function [tex]\( C(F) \)[/tex] will convert a temperature from Fahrenheit back to Celsius.
