# Create two functions f and g
def f(x): return(x**2+2) def g(x): return(3*x1)
# Create the composite function f(g(x)) and call it composite_fg. You can solve for f(g(x)) on paper.
def composite_fg(x): return(9*x**26*x+3)
# Compute f(g(3)) using both functions f and g separately and by using composite_fg. Are they equal?
print(f(g(3))) print(composite_fg(3))
# Create the composite function g(f(x)) and call it composite_gf.
def composite_gf(x): return(3*x**2+5)
# Compute g(f(5)) using both functions g and f separately and by using composite_gf. Are they equal?
print(g(f(5))) print(composite_gf(5))
# Examples
# You work forty hours a week at a furniture store. You receive a $220 weekly salary, plus a 3% commision on sales over $5000. Assume that you sell enough this week to get the commission. Use composite functions to calculate how much you take home in commission when you sell $8000.
def amount_over(sales): return sales  5000 def commision(amt): return amt*0.03
print(commision(amount_over(8000)))
# You make a purchase at a local hardware store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales taxes, plus the fee. The taxes are 7.5% and the fee is $20. # Part a  Write a function t(x) for the total, after taxes, on the purchase amount x. Write another function d(x) for the total, including the delivery fee, on the purchase amount x.
def t(x): return(x + 0.075*x) def d(x): return(x+20) # Part b  Calculate and interpret d(t(x)) and t(d(x)). Which results in a lower cost to you?
print(d(t(20))) print(t(d(20)))
# ANSWER d(t(x)) results in a lower cost because the tax is not being applied to the delivery fee
# Part c  Suppose taxes, by law, are not to be charged on delivery fees. Which composite function must then be used?
# ANSWER d(t(x) must be used
