Question

The function f(x) = 5/9 (x − 32) can be used to determine the temperature in °C when the temperature is x°F. Find the inverse function that can be used to determine the temperature in °F when the temperature is x°C. The function that can determine the temperature in °F is f⁻¹(x) = ?

Answer 1

The inverse function for converting Celsius to Fahrenheit is f⁻¹(x) = (9/5)x + 32. This is obtained by manipulating the original Celsius to Fahrenheit conversion formula and solving for the Fahrenheit variable.

Step-by-step explanation:

To find the inverse function that converts Celsius to Fahrenheit, we start with the original function f(x) = (5/9)(x - 32), where x is in Fahrenheit. From this function, we solve for x in terms of f(x), which represents Celsius, to find the inverse function.

1. First, replace f(x) with y for simplicity: y = (5/9)(x - 32).
2. Multiply both sides by 9/5 to get (9/5)y = x - 32.
3. Add 32 to both sides to isolate x: x = (9/5)y + 32.
4. Finally, replace y with f-1(x) to get the inverse function: f-1(x) = (9/5)x + 32.

This inverse function can be used to convert Celsius to Fahrenheit, and it is represented by f-1(x) = (9/5)x + 32.