To find the inverse of the function \(f(c) = \frac{9}{5} c + 32\), which converts degrees Celsius to degrees Fahrenheit, we will follow these steps:
1. Start with the given function:
[tex]\[
f(c) = \frac{9}{5} c + 32
\][/tex]
2. To find the inverse, we need to express \(c\) in terms of \(f\).
3. Set \(f(c)\) equal to \(y\):
[tex]\[
y = \frac{9}{5} c + 32
\][/tex]
4. Solve for \(c\) in terms of \(y\):
Start by isolating the term with \(c\):
[tex]\[
y - 32 = \frac{9}{5} c
\][/tex]
Now, to solve for \(c\), multiply both sides of the equation by the reciprocal of \(\frac{9}{5}\), which is \(\frac{5}{9}\):
[tex]\[
c = \frac{5}{9} (y - 32)
\][/tex]
5. Replace \(y\) with \(f\) to denote the inverse function:
[tex]\[
c(f) = \frac{5}{9} (f - 32)
\][/tex]
After these steps, we find that the inverse function to convert from degrees Fahrenheit back to degrees Celsius is:
[tex]\[
c(f) = \frac{5}{9} (f - 32)
\][/tex]
Given the options:
- A. \(c(f) = \frac{9}{5} (f + 32)\)
- B. \(c(f) = \frac{5}{9} (f - 32)\)
- C. \(c(f) = \frac{9}{5} (f - 32)\)
- D. \(c(f) = \frac{5}{9} (f + 32)\)
The correct answer is:
[tex]\[
\boxed{\text{B}}
\][/tex]
