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) $f(-2)$

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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) $h(15)$

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a) $44$   b) $-4$   c) $4$   d) $220$

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) $gg(-2)$

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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) $hh(40)$

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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) $hgf(x)$

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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) $64x^2$

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

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

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

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

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