# Composite Function Exam Questions

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Functions - Composite functions (L6) Core 3 Edexcel A-Level
A composite function is when two or more functions combine.
Examples:
The functions f,g, and h are defined for x ∈ ℝ, by
f(x) = 2x + 1, g(x) = x2, h(x) = 1/x.
Find
(i) fg(2)
(ii) gf(3)
(iii) gf(x)
(iv) fg(x)
(v) f2(x)
(vi) g2(x)
(vii) h2(x)
(viii) fgh(x)

A-Level Edexcel C3 January 2008 Q8(b) : ExamSolutions
Worked solution to this question on composite function.
Example:
Given f:x ↦ 1 - 2x2 and g: ↦ 3/x - 4
find gf(x)

A-Level Edexcel C3 January 2010 Q9ii(b)
Worked solution to this question on composite functions.
f(x) = e2x + 3, x ∈ ℝ
g(x) = ln(x -1), x ∈ ℝ, x > 1
Find fg(x)

Composite functions - (IB Math, GCSE, A level, AP)
f(x) = x - 2, g(x) = 3x2 + 1
a) what is (f￮g)(x)?
b) what is f(g(2))?
c) what is g(f(x))?

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