Composition feeds the output of one rule into another, and order matters.
WHAT HAPPENS IF…With x=1, a=2, b=1, do the two orders agree?
Interactive exploration
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Connect the picture to the idea(f∘g)(x)=f(g(x))=(ax+b)2
Apply the inner function first. For f(x)=x² and g(x)=ax+b, f(g(x))=(ax+b)². Reversing the order gives g(f(x))=ax²+b. The two rows expose both intermediate values, so the calculation can be checked step by step.