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Let \( f(x)=2 x+2 \) and \( g(x)=3 x^{2}+2 x \) After simplifying, \( (f \circ g)(x)=\square \)

Ask by Harris Riley. in the United States
Feb 26,2025

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\( (f \circ g)(x) = 6x^{2} + 4x + 2 \)

Solución

To find (f ∘ g)(x), we substitute g(x) into f(x): 1. Write down the functions:   f(x) = 2x + 2   g(x) = 3x² + 2x 2. Substitute g(x) into f(x):   (f ∘ g)(x) = f(g(x)) = 2(3x² + 2x) + 2 3. Simplify the expression:   = 6x² + 4x + 2 Thus, (f ∘ g)(x) = 6x² + 4x + 2.

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Bonus Knowledge

To find \( (f \circ g)(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we have \( g(x) = 3x^2 + 2x \). Now, substituting \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(3x^2 + 2x) = 2(3x^2 + 2x) + 2 \] Now, simplify this expression: \[ = 6x^2 + 4x + 2 \] Therefore, \( (f \circ g)(x) = 6x^2 + 4x + 2 \).

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