Functions and Iteration

This lesson covers function notation, composite functions, inverse functions, and iteration — all Higher tier topics in the Edexcel GCSE (1MA1) specification.

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Key Vocabulary

Term	Meaning
Function	A rule that maps each input to exactly one output
f(x)	"f of x" — the output when x is the input to function f
Domain	The set of allowed inputs
Range	The set of possible outputs
Composite function	Applying one function then another: fg(x) means do g first, then f
Inverse function	The function that reverses f; written f⁻¹(x)
Iteration	Repeatedly applying a formula to get closer to a solution

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Function Notation

When we write f(x) = 3x + 1, this means: "the function f takes an input x and gives the output 3x + 1."

Worked Example 1

f(x) = 2x² − 3x + 1

Find: (a) f(4) (b) f(−2) (c) f(0)

(a) f(4) = 2(16) − 3(4) + 1 = 32 − 12 + 1 = 21