Algebra and functions

WMA13Topic 3.13 questions

Rational expressions, functions, inverse and composite functions, and the modulus function.

Specification points

Specification points for this topic are coming soon.

Get a plain-language explanation, a worked example and the usual mistake.

Sign in to get a plain-language explanation of any specification point.

Original practice questions written in the style of the exam.

Question 14 marks
The function $f$ is defined by

$f(x) = \frac{2x + 3}{x - 1}, \quad x > 1$

Find $f^{-1}(x)$ , stating its domain.
Mark scheme
- M1 Sets $y = \dfrac{2x + 3}{x - 1}$ and multiplies out: $xy - y = 2x + 3$ (1)
Question 24 marks
Solve the equation $|x - 5| = 2x - 1$ .
Mark scheme
- M1 Solves $x - 5 = 2x - 1$ to get (1)

xy−

y=

2x+

3

M1 Collects

x

terms and factorises:

x(y - 2) = y + 3

(1)

A1

f^{-1}(x) = \dfrac{x + 3}{x - 2}

(1)

B1 Domain

x > 2

(1)

5

=

2x−

1

x = -4

M1 Solves

-(x - 5) = 2x - 1

to get

x = 2

(1)

A1

x = 2

(1)

A1 Rejects

x = -4

because it makes

2x - 1

negative, which a modulus cannot equal (1)