# AQA PC3 Overview

Key things to know for PC3 AQA Maths

- Created by: TheDitzyBlonde
- Created on: 15-01-11 16:19

First 224 words of the document:

Functions

Domain and range

Domain is the set of permitted x-values

Range is the set of permitted y-values f(x) values

x=R means x can be any of the reals

f(x)=R means f(x) can be any of the reals

Mappings

Show relationship between x and y-values

Ono-to-one mapping = each x-value mapped to a single y-value

One-to-many mapping = each x-value mapped to several y-values

Many-to-one mapping = several x-values map onto the same y-value

Many-to-many mapping = each x and y-value mapped to several other values

Modulus

|x| is an absolute value function; y-values always positive

Solve by squaring each side, or by considering each non-modulus value as both positive and

negative

Composite functions

One function followed by another

f(x) followed by g(x) = gf(x)

Inverse functions

To find inverse, swap x and y-values over in the f(x) equation

Domain of inverse = range of original

Range of inverse = domain of original

Can only find inverse for one-to-one or one-to-many mappings

Inverse is a reflection in the line y=x of the original function

Inverse trigonometric functions can be found if you restrict the domain to make the original

function a one-to-one mapping

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