Question

The oven temperature for making breads and other baked goods at elevations over 2,500 feet should be 30°F higher than the temperature used at sea level (so F(t) = t + 30). The conversion from Fahrenheit to Celsius is C(t) = (t – 32), where t is the temperature in degrees Fahrenheit. Write a composite function to represent the oven temperature at elevations over 2,500 feet in Celsius.

Answer 1

To represent the oven temperature at elevations over 2,500 feet in Celsius, we can use the composite function F(C(t)) = (C(t) + 30). This means we first convert the Fahrenheit temperature to Celsius and then add 30 to it. For example, if the Fahrenheit temperature is 80°F, the temperature at elevations over 2,500 feet would be 78°C.

Step-by-step explanation:

To write a composite function to represent the oven temperature at elevations over 2,500 feet in Celsius, we can use the given functions F(t) = t + 30 and C(t) = (t - 32). Since we want to represent the temperature at elevations over 2,500 feet in Celsius, we need to convert the Fahrenheit temperature to Celsius using the C(t) function first. Then, we can apply the F(t) function to get the temperature with the 30°F increase.

The composite function can be written as F(C(t)) = (C(t) + 30). This means that we first convert the Fahrenheit temperature to Celsius and then add 30 to it.

For example, if the Fahrenheit temperature at elevations over 2,500 feet is 80°F, we can convert it to Celsius using the C(t) function: C(80) = (80 - 32) = 48°C. Then, we apply the F(t) function to get the temperature with the 30°F increase: F(48) = (48 + 30) = 78°C.