Answer:
[tex]C(T(x))=1.15x-5[/tex] and [tex]T(C(x))=1.15x-5.75[/tex]
C(T(x)) represents the conditions of the coupon.
Step-by-step explanation:
The price after the coupon reduction is represented by the function
[tex]C(x)=x-5[/tex]
The price after the tip is applied is represented by the function
[tex]T(x)=1.15x[/tex]
We need to find the composite functions C(T(x)) and T(C(x)).
[tex]C(T(x))=C(1.15x)[/tex] [tex][\because T(x)=1.15x][/tex]
[tex]C(T(x))=1.15x-5[/tex] [tex][\because C(x)=x-5][/tex]
This function represents that 15% tip will be added first after that $5 is subtracted.
Similarly,
[tex]T(C(x))=T(x-5)[/tex] [tex][\because C(x)=x-5][/tex]
[tex]T(C(x))=1.15(x-5)[/tex] [tex][\because T(x)=1.15x][/tex]
[tex]T(C(x))=1.15x-5.75[/tex]
This function represents that $5 is subtracted first after that 15% tip will be added.
It is given that a coupon for $5 off any lunch price states that a 15% tip will be added to the price before the $5 is subtracted.
It means 15% tip will be added first after that $5 is subtracted. So, C(T(x)) represents the conditions of the coupon.
