Composite Functions (Leaving Cert Mathematics): Revision Notes

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Composite Functions

A composite function is created when one function is applied to the result of another function. If you have two functions f(x)f(x) and g(x)g(x), the composite function f(g(x))f(g(x)) means that you first apply g(x)g(x), then use the result as the input for f(x)f(x).

The composition of f(x)f(x) and g(x)g(x) can be written as :

(f∘g)(x)=f(g(x))(f \circ g)(x)=f(g(x))

This is read as "ff after gg" , that is, apply f(x)f(x) after you applied g(x)g(x).

Example

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f(x)=2x+1f(x)=2x+1 and g(x)=x2g(x)=x^2, find (f∘g)(x)(f \circ g)(x)

f(g(x))=f(x2)=2(x2)+1=2x2+1f(g(x))=f(x^2)=2(x^2)+1=2x^2+1

Find (f∘g)(3)(f \circ g)(3)

f(g(3))=2(3)2+1=19f(g(3))=2(3)^2+1=19
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The key idea is that the function closest to the bracket is the one that gets applied first (the most nested function).

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Fundamentals of Functions

The Basics

Types of Graphs

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Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

Explore Leaving Cert Mathematics Quizzes by Topics

Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

Explore Leaving Cert Mathematics Flashcards by Topics

Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

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