Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: Substituting Functions into Functions
Function composition is the process of substituting one function into another. The notation (f ∘ g)(x) means f(g(x))—first apply g to x, then apply f to the result.
While the notation may appear intimidating at first, the concept is straightforward: wherever the outside function has a variable, replace it with the entire inside function.
Review: Function Notation
Function notation provides a way to name functions and substitute values.
If f(x) = 4x - 1, then:
- f(w) = 4w - 1
- f(6) = 4(6) - 1 = 23
- f(smiley) = 4(smiley) - 1
The pattern is consistent: substitute whatever appears in parentheses for x in the function rule.
Composing Functions
Composition means substituting one function into another.
Example 1: Basic Composition
Let f(x) = 4x - 1 and g(x) = 3x².