Mathematics — first biennium · Lesson
Composing two functions means using the output of the inner function as the input of the outer function. Order matters.
Prerequisites: Functions and representations
Goal: Calculate f(g(x)) by distinguishing inner and outer functions and understand that composition order matters.
In this lesson: Calculate f(g(x)) by distinguishing inner and outer functions and understand that composition order matters.
New concept: In the composition (f∘g)(x)=f(g(x)), g is the inner function: it produces the value that becomes the input of f. Order is part of the operation, and in general f∘g and g∘f are different functions.
How to proceed: Follow the parentheses from the inside out: calculate g(x), then substitute that value into f.
You can already assume: Functions and representations.
Completed exercises: 0/5 · Correct on first attempt: 0
Follow the parentheses from the inside out: calculate g(x), then substitute that value into f.
Data / situation: f(x)=x−4, g(x)=-3x−2. Compute (f∘g)(-2).
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.