How to solve this problem please

Question

Find the function of function or compound function f[g(x)] and g[f(x)] corresponding to the following problem: A store that wants to promote its sales advertises a reduction in the price of certain items of 30%. It also advertises another $50 rebate on each item from a certain vendor.

-Write the function that corresponds to the 30% discount, name it f (x).

-Write the function that corresponds to the $ 50 discount, name the same g (x)

-For the items that get both discounts at the same time, make the composition of the functions in both directions f [g (x)] and g [f (x)]

-The starting price of an item is $ 500. Apply the two compound functions to it. Is it the same price? And if it is not, why is the difference?

Answer 1

g(x) = 0.7 x - 50

g(500) = 0.7*500 - 50 = 350-50 = 300