Question

You have a $20 coupon from the manufacturer that is good for the purchase of a cell phone. Look at my picture for the rest of the question

Answer 1

item (a):

Since we're going to have a 10% discount, it means the final price of the phone should be 90% of the regular price. To calculate 90% of a quantity is the same as multiplying by 0.9. This means our function can be modeled as

$f(x)=0.9x$

item (c):

We have the following two functions

$\begin{gathered} f(x)=0.9x \\ g(x)=x-20 \end{gathered}$

To calculate the compositions

$\begin{gathered} (f\circ g)(x) \\ (g\circ f)(x) \end{gathered}$

We just need to use one of the functions as the argument of the other.

$(f\circ g)(x)=f(g(x))=f(x-20)=0.9(x-20)=0.9x-18$

Doing the same for the other order

$(g\circ f)(x)=g(f(x))=g(0.9x)=0.9x-20$