4-2 Operations on Functions Homework: Pages 128-130, #1, 3, 5-10, 17-19, 23-26, 33, 35 Just like real numbers, you can add subtract, multiply, and divide functions to create NEW functions. Let f and g be two functions with overlapping domains. Then for all x common to both domains:

Sum Example TI-84?

Difference Example TI-84?

Product Example TI-84?

Quotient Example

Composition Composition Example

More Composition

Doublecheck: Finding the Domain of a Composition

Do you remember this special case? What does it mean? If f(g(x)) = g(f(x)) = x, then the two functions are inverses of each other! Graphically, the functions are symmetric about the line y = x.

Decomposing? In calculus, it will become important to be able to identify two functions that make up a given composite function. Basically, to “decompose” a composite function, look for an “inner” and an “outer” function. h(x) = (3x – 5)3 f(x) = x3 g(x) = 3x – 5 h(x) = f(g(x))

You Try It!

Who does this stuff?