Last updated on Oct 23, 2026

Composite Functions (HSC SSCE Mathematics Advanced): Quizzes

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Composite Functions

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What is a composite function?

Output of one function is input of another

In $f(g(x))$ , which function is applied first?

$g(x)$ is applied first

Is it generally true that $f(g(x)) = g(f(x))$ for all functions?

No, order of composition affects result

If $f(x) = 3x - 2$ and $g(x) = x^2 + 1$ , what is $f(g(x))$ ?

$3x^2 + 1$

If $f(x) = 2x + 1$ and $g(x) = x^2$ , what is $f(g(3))$ ?

$19$

What determines the domain of $g(f(x))$ ?

Domain of $f$ and valid inputs for $g$

If $f(x) = 3x - 1$ and $g(x) = \sqrt{x}$ , what is the domain of $g(f(x))$ ?

$[\frac{1}{3}, \infty)$

If $f(x) = x + 5$ and $g(x) = 2x$ , what is $g(f(x))$ ?

$2x + 10$

What determines the range of $f(g(x))$ ?

Range of $f$ , restricted by output of $g$

If $f(x) = x^2$ and $g(x) = x + 1$ , does $f(g(2)) = g(f(2))$ ?

No, $f(g(2)) = 9$ but $g(f(2)) = 5$

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Composite Functions (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What is a composite function?

In f(g(x))f(g(x))f(g(x)), which function is applied first?

Is it generally true that f(g(x))=g(f(x))f(g(x)) = g(f(x))f(g(x))=g(f(x)) for all functions?

If f(x)=3x−2f(x) = 3x - 2f(x)=3x−2 and g(x)=x2+1g(x) = x^2 + 1g(x)=x2+1, what is f(g(x))f(g(x))f(g(x))?

If f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and g(x)=x2g(x) = x^2g(x)=x2, what is f(g(3))f(g(3))f(g(3))?

What determines the domain of g(f(x))g(f(x))g(f(x))?

If f(x)=3x−1f(x) = 3x - 1f(x)=3x−1 and g(x)=xg(x) = \sqrt{x}g(x)=x​, what is the domain of g(f(x))g(f(x))g(f(x))?

If f(x)=x+5f(x) = x + 5f(x)=x+5 and g(x)=2xg(x) = 2xg(x)=2x, what is g(f(x))g(f(x))g(f(x))?

What determines the range of f(g(x))f(g(x))f(g(x))?

If f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x+1g(x) = x + 1g(x)=x+1, does f(g(2))=g(f(2))f(g(2)) = g(f(2))f(g(2))=g(f(2))?

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Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

In $f(g(x))$ , which function is applied first?

Is it generally true that $f(g(x)) = g(f(x))$ for all functions?

If $f(x) = 3x - 2$ and $g(x) = x^2 + 1$ , what is $f(g(x))$ ?

If $f(x) = 2x + 1$ and $g(x) = x^2$ , what is $f(g(3))$ ?

What determines the domain of $g(f(x))$ ?

If $f(x) = 3x - 1$ and $g(x) = \sqrt{x}$ , what is the domain of $g(f(x))$ ?

If $f(x) = x + 5$ and $g(x) = 2x$ , what is $g(f(x))$ ?

What determines the range of $f(g(x))$ ?

If $f(x) = x^2$ and $g(x) = x + 1$ , does $f(g(2)) = g(f(2))$ ?