Last updated on Oct 23, 2026

Operations Involving Functions (Leaving Cert Mathematics): Quizzes

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Operations Involving Functions

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Which notation is NOT equivalent to $f(x) = 2x + 1$ ?

$f(2x + 1) = x$

What does the notation $f(5)$ represent?

The output value when input is 5

If $f(x) = 3x - 2$ , what is $f(3)$ ?

$7$

If $f: x → x + 5$ , what is $f(k + 1)$ ?

$k + 6$

What does the composite function notation $gf$ mean?

$g$ after $f$

Is it true that $fg(x) = gf(x)$ for any two functions $f$ and $g$ ?

No, order matters

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

$6$

If $f(x) = 2x + 5$ and $g(x) = x - 3$ , what is $gf(x)$ ?

$2x + 2$

In the notation $gf(x)$ , which function do you apply first?

$f$

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

$3$

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

$x^2 + 2$

If $f(x) = 2x + 5$ and $g(x) = x - 3$ , does $fg(x)$ equal $gf(x)$ ?

No, $fg(x) = 2x - 1$ & $gf(x) = 2x + 2$

Explore Leaving Cert Mathematics Revision Notes by Topics

Fundamentals of Functions

The Basics

Types of Graphs

Graph Transformations

Injective, Surjective & Bijective Functions

Composite Functions

Inverse Functions

Explore Leaving Cert Mathematics Model Answers 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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