Question
Let \( f(x)=5 x+2 \) and \( g(x)=3 x^{2}+2 x \) After simplifying, \( (f \circ g)(x)=\square \)
Ask by Alexander Weaver. in the United States
Mar 14,2025
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Answer
\( (f \circ g)(x) = 15x^2 + 10x + 2 \)
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Bonus Knowledge
To simplify \( (f \circ g)(x) \), we need to substitute \( g(x) \) into \( f(x) \): 1. Start with \( g(x) = 3x^2 + 2x \). 2. Then compute \( f(g(x)) = f(3x^2 + 2x) = 5(3x^2 + 2x) + 2 \). 3. Distribute \( 5 \) within the parentheses: \( = 15x^2 + 10x + 2 \). So, \( (f \circ g)(x) = 15x^2 + 10x + 2 \).