Answer :
The expression to determine how high to preheat your oven when a recipe calls for a temperature of [tex]t^{\circ} C[/tex] is [tex]\frac{9}{5}t + 17[/tex].
To solve this problem, you'll need to use a composition of functions that first converts the Celsius temperature to Fahrenheit, and then adjusts the temperature for your oven.
Convert Celsius to Fahrenheit:
The formula to convert from degrees Celsius [tex]C[/tex] to degrees Fahrenheit [tex]F[/tex] is:
[tex]F = \frac{9}{5}C + 32[/tex]Here, we will define a function [tex]f(C)[/tex] that represents this conversion:
[tex]f(C) = \frac{9}{5}C + 32[/tex]Adjust the Oven Temperature:
Since your oven runs hot and you need to decrease the temperature by [tex]15^{\circ} F[/tex], we'll create a function [tex]g(F)[/tex] to account for this:
[tex]g(F) = F - 15[/tex]Compose the Functions:
To find the temperature to which you should preheat your oven, apply the oven adjustment function to the temperature obtained from the conversion function. This composition of functions is represented as [tex]g(f(C))[/tex]:
[tex]g(f(C)) = \left( \frac{9}{5}C + 32 \right) - 15[/tex]Simplifying the expression:
[tex]g(f(C)) = \frac{9}{5}C + 17[/tex]
The expression for how high to preheat your oven in Fahrenheit when the recipe calls for [tex]\(t^\circ C\)[/tex] is F = 9/5t + 17
The conversion formulas are given as follows
- Celsius to Fahrenheit: F = 9/5C + 32
- Fahrenheit to Celsius: C = 5/9(F - 32)
First, we convert the temperature to Fahrenheit (F)
We use the formula F = 9/5C + 32, where [tex]\( C = t^\circ C \)[/tex]:
F = 9/5t + 32
Since the oven runs hot by 15°F, we subtract 15°F from the result:
F = 9/5t + 32 - 15
F = 9/5t + 17
