The temperature in degrees Fahrenheit, F(c), can be converted to degrees Celsius using the formula C(c) = (F(c) - 32) / 1.8. What is the inverse function, C-1(c), that represents the temperature in degrees Fahrenheit for a given temperature of c degrees Celsius?
Question
The temperature in degrees Fahrenheit, F(c), can be converted to degrees Celsius using the formula C(c) = (F(c) - 32) / 1.8. What is the inverse function, C-1(c), that represents the temperature in degrees Fahrenheit for a given temperature of c degrees Celsius?
Solution
The inverse function, F(c), that represents the temperature in degrees Fahrenheit for a given temperature of c degrees Celsius can be found by rearranging the original formula.
Step 1: Start with the original formula: C(c) = (F(c) - 32) / 1.8
Step 2: Multiply both sides by 1.8 to isolate F(c) on one side: 1.8 * C(c) = F(c) - 32
Step 3: Add 32 to both sides to solve for F(c): F(c) = 1.8 * C(c) + 32
So, the inverse function is F(c) = 1.8 * C(c) + 32. This function represents the temperature in degrees Fahrenheit for a given temperature of c degrees Celsius.
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