Functions and Algebraic Fractions [H]

This lesson covers Higher tier content on function notation, composite functions, inverse functions, and algebraic fractions. These topics are among the most challenging in the AQA GCSE Mathematics specification and are frequently tested in the later questions on the Higher paper. A solid understanding here will also provide an excellent foundation for A-level Mathematics.

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Function Notation

A function is a rule that maps each input to exactly one output. In GCSE Mathematics, functions are written using the notation:

f(x) = ... or g(x) = ...

The letter before the bracket names the function; the letter inside the bracket is the input (usually x).

Worked Example 1

f(x) = 3x + 2

(a) Find f(4).

Replace x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14

(b) Find f(-3).

f(-3) = 3(-3) + 2 = -9 + 2 = -7

(c) Find the value of x when f(x) = 20.

3x + 2 = 20

3x = 18

x = 6

Worked Example 2

g(x) = x^2 - 4x + 1

Find g(5).