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{5}{9}(f-32)[/tex]
B. [tex]c(f)=\frac{9}{5}(f+32)[/tex]
C. [tex]c(f)=\frac{5}{9}(f+32)[/tex]
D. [tex]c(f)=\frac{9}{5}(f-32)[/tex]
Answer (1)
Replace f ( c ) with f : f = 5 9 c + 32 .
Solve for c in terms of f : c = 9 5 ( f − 32 ) .
Replace c with c ( f ) to express the inverse function: c ( f ) = 9 5 ( f − 32 ) .
The inverse function is c ( f ) = 9 5 ( f − 32 ) .
Explanation
Understanding the Problem We are given the function f ( c ) = 5 9 c + 32 that converts degrees Celsius to degrees Fahrenheit. Our goal is to find the inverse function c ( f ) that converts degrees Fahrenheit back to degrees Celsius.
Replacing f(c) with f To find the inverse function, we first replace f ( c ) with f , so we have f = 5 9 c + 32 .
Isolating the term with c Next, we solve for c in terms of f . Subtract 32 from both sides of the equation: f − 32 = 5 9 c
Solving for c Multiply both sides by 9 5 to isolate c : c = 9 5 ( f − 32 )
Writing the Inverse Function Finally, replace c with c ( f ) to denote the inverse function: c ( f ) = 9 5 ( f − 32 ) This is the inverse function that converts degrees Fahrenheit to degrees Celsius.
Selecting the Correct Option Comparing our result with the given options, we see that it matches option A.
Examples
Imagine you're traveling to a country that uses Celsius, but you're used to Fahrenheit. The formula we derived helps you convert the local temperature back to Fahrenheit so you can understand how hot or cold it is. This is a practical example of using inverse functions in everyday life. Similarly, if you are a scientist and need to convert between temperature scales for your experiments, this formula becomes essential. Understanding inverse functions allows for easy conversion and comprehension in various real-world scenarios.
