Answered

The function [tex]$f(c)=\frac{9}{5} c + 32$[/tex] allows you to convert degrees Celsius to degrees Fahrenheit. Find the inverse of the function so that you can convert degrees Fahrenheit back to degrees Celsius.

A. [tex]$c(f)=\frac{9}{5}(f+32)$[/tex]
B. [tex]$c(f)=\frac{5}{9}(f-32)$[/tex]
C. [tex]$c(f)=\frac{9}{5}(f-32)$[/tex]
D. [tex]$c(f)=\frac{5}{9}(f+32)$[/tex]



Answer :

GinnyAnswer
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]

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