Finding (f ∘ g)(x) where f(x) = x² + 1 and g(x) = 2x - 3

Algebra 2 · Axiom Academy

EXAMPLE Finding Where f(x) = x^2+1 and g(x) = 2x-3 Learn how to compose functions step-by-step by substituting one function into another. Given the functions f(x) = x^2 + 1 and g(x) = 2x - 3 , find . Excellent work! You've mastered function composition. Here's what to remember: Composition means substitution, not multiplication: — it is NOT . Composing two functions substitutes one into the other; it never multiplies them. Order matters: is usually different from . Substitution is key: replace every x in f(x) with the entire expression for g(x) . Don't forget parentheses: when substituting (2x - 3) , write (2x-3)^2 , not 2x-3^2 . Simplify completely: expand and combine like terms for the final answer. Practice Tip: Try reversing the order and find with the same functions. You'll get a different result!

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