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# GCSE Maths | Functions
- URL: https://www.a-level-maths-tutor.com/gcse-maths-functioins/
- Published: 2026-09-27T15:00:24.000Z
- Updated: 2026-09-27T15:00:24.000Z
- Author: Jaisul Naik
- Tags: GCSE Maths

Functions

## Question 1

Given $f(x) = 3x + 5$, work out the values of

**a)** $f(2)$

**b)** $f(8)$

**c)** $f(0)$

**d)** $f(-2)$

Show Answers 

**a)** $11$ **b)** $29$ **c)** $5$ **d)** $-1$

## Question 2

Given $h(x) = x^2 - 5$, work out the values of

**a)** $h(7)$

**b)** $h(-1)$

**c)** $h(-3)$

**d)** $h(15)$

Show Answers 

**a)** $44$ **b)** $-4$ **c)** $4$ **d)** $220$

Composite Functions

## Question 3

The functions $f(x)$ and $g(x)$ are given by the following:

$f(x) = x + 5$

$g(x) = 3x - 1$

Calculate the value of:

**a)** $fg(1)$

**b)** $fg(-5)$

**c)** $gf(4)$

**d)** $gf(0)$

**e)** $ff(2)$

**f)** $ff(-4)$

**g)** $gg(10)$

**h)** $gg(-2)$

Show Answers 

**a)** $7$ **b)** $-11$ **c)** $26$ **d)** $14$

**e)** $12$ **f)** $6$ **g)** $86$ **h)** $-22$

## Question 4

The functions $f(x)$, $g(x)$ and $h(x)$ are given by the following:

$f(x) = x^2 + 7$

$g(x) = 3x - 8$

$h(x) = \\dfrac{x}{4}$

Calculate the value of:

**a)** $fg(3)$

**b)** $hf(5)$

**c)** $gh(20)$

**d)** $gf(-2)$

**e)** $fh(12)$

**f)** $ff(1)$

**g)** $gg(4)$

**h)** $hh(40)$

Show Answers 

**a)** $8$ **b)** $8$ **c)** $7$ **d)** $25$

**e)** $16$ **f)** $71$ **g)** $4$ **h)** $2.5$

## Question 5

The functions $f(x)$, $g(x)$ and $h(x)$ are given by the following:

$f(x) = 4x - 3$

$g(x) = 2x + 6$

$h(x) = x^2$

Find

**a)** $fg(x)$

**b)** $gf(x)$

**c)** $hf(x)$

**d)** $fh(x)$

**e)** $hg(x)$

**f)** $gh(x)$

**g)** $fgh(x)$

**h)** $hgf(x)$

Show Answers 

**a)** $8x + 21$ **b)** $8x$ **c)** $16x^2 - 24x + 9$ **d)** $4x^2 - 3$

**e)** $4x^2 + 24x + 36$ **f)** $2x^2 + 6$ **g)** $8x^2 + 21$ **h)** $64x^2$

Inverse Functions

## Question 6

For each of the following functions find an expression for its inverse.

**a)** $f(x) = 4x - 1, \\quad x \\in \\mathbb{R}$

**b)** $g(x) = 1 + \\sqrt{x}, \\quad x \\in \\mathbb{R},\\ x \\geq 0$

**c)** $h(x) = 1 - \\sqrt{x - 5}, \\quad x \\in \\mathbb{R},\\ x \\geq 5$

Show Answers 

**a)** $f^{-1}(x) = \\dfrac{x + 1}{4}$

**b)** $g^{-1}(x) = (x - 1)^2$

**c)** $h^{-1}(x) = 5 + (1 - x)^2$

## Question 7

For each of the following functions find an expression for its inverse.

**a)** $f(x) = 5 - 2x, \\quad x \\in \\mathbb{R}$

**b)** $g(x) = \\dfrac{3}{x} - 2, \\quad x \\in \\mathbb{R},\\ x \\neq 0$

**c)** $h(x) = \\sqrt{\\dfrac{x}{2} - 1}, \\quad x \\in \\mathbb{R},\\ x \\geq 2$

Show Answers 

**a)** $f^{-1}(x) = \\dfrac{5 - x}{2}$

**b)** $g^{-1}(x) = \\dfrac{3}{x + 2}$

**c)** $h^{-1}(x) = 2x^2 + 2$

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