Lesson 2: 5-2 Composition of Functions

How does f(g(x)) differ from g(f(x))?
How can you rewrite fog(5) to make it easier to evaluate?
How is f(g(5)) similar to working with the order of operations?
What must be true about the domain of f(x) and g(x) in order for the value of the f(g(x)) to exist?

composition of functions

F.BF.1c Compose functions

See below

Composition of functions is a process of using one function as an input for a second function. It is fundamentally different from arithmetic operations on functions. For example, in composition g(f(x)), the output f(x) is used as the input for g.

Submersibles can descend several miles below the surface of the ocean. You can write a function d(t) that gives the depth of the submersible after t minutes and a function p(d) that gives the pressure at the depth d. The composition of the functions p(d(t) gives the pressure on the submersible after t minutes.

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Have students write expressions that involve compositions of functions and then annotate the expressions with notes to themselves such a "f(g(x)) is pronounced f of g of x and Start by finding the value of g(x), then use that value as the input for f."

Use McGraw Hill Resources

Use McGraw Hill Resources

SAT Practice chapter 5