Lessons on Composition and Combination of Functions

Fancy ways of combining like terms, multiplying and dividing polynomials, and performing substitution.

• Review combining functions using algebraic operations.

• Evaluate composite functions.

• Create a new function by composition of functions.

h(t) = 5 ------------> h(4) = 5

t is the input

h(t) is the output

(input, output)

(t, h(t))

(4, 5)

Fancy word for SUBSTITUTION!

On November 25th, a store selling very expensive clothing will sell any item for $50 less than the listed price. On any day in November, the store will give a discount of 15% to any customer who can prove that he/she contributed to a local charity. You go to the store on November 25th with evidence you have donated to a local charity. Is it better for you to subtract $50 and then apply 15% discount or apply 15% discount and then subtract $50? Explain.

• Fancy term for substitution. (Performed at least twice)

• A composite function is created when one function is substituted into another function.

• A composite function consists of applying one rule, getting a result, and then applying a second rule to the result obtained from the first rule.

• Decisions are made in which the order or sequence of application can and will make a difference.

The key idea in function composition is the input of the function is NOT a numerical value, instead the INPUT is ANOTHER FUNCTION.

• Step 1: Substitute 4 for x in g(x)

• g(4) = 3(4)²

• g(4) = 3(16)

• g(4) = 48

• Step 2: Substitute 48 into f(x).

• f(48) = 5(48) + 3

• f(48) = 240 + 3 = 243 ... f(g(4)) = 243