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Why g ∘ f ≠ f ∘ g | Function Composition Example
In this short math video, I compute (g ∘ f)(x) = g(f(x)) using f(x) = x² + 2x − 3 and g(x) = −3x + 2. After carefully substituting the entire expression into g and simplifying, we find g(f(x)) = −3x² − 6x + 11. This result is different from what we found earlier for (f ∘ g)(x) = f(g(x)) = 9x² − 18x + 5, showing that function ...
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