This animation shows how to build a composite function by substituting one function into another. Using f(x)=2x+5 and g(x)=x-6, it walks through finding fg(x) by replacing x in f(x) with g(x), simplifying the expression line by line with color-coded substitution. A matching practice problem, finding gf(x), reinforces the order matters in composition. Ideal for O Level, IGCSE, and GCSE Edexcel students learning function notation and composition rules.
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Explain concept of composite function. A composite function means putting one function inside another function. Let's discuss an example: Given that f(x)=2x+5 and g(x)=x-6. Find fg(x). Solution: There are two functions f and g. In fg(x), the first function is f(x)=2x+5. Put g(x)=x-1 into f. fg(x)=5(x-1)-6 =5x-5-6 fg(x)=5x-11 Now it's your turn, find gf(x). Audience: O level, IGCSE, GCSE EDEXCEL Mathematics students