Question
Using the following equations, find \( f(g(x)) \) : \( f(x)=-2 x \) \( g(x)=x^{2}+3 \) \( \left.f(g(x))=[?] x^{2}+\square\right] \)
Ask by Wagner Luna. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(x)) = -2x^2 - 6 \)
Solution
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The Deep Dive
To find \( f(g(x)) \), we start by substituting \( g(x) \) into \( f(x) \). Given \( g(x) = x^2 + 3 \), we have: \[ f(g(x)) = f(x^2 + 3) \] Now, substitute \( x^2 + 3 \) into the function \( f(x) = -2x \): \[ f(x^2 + 3) = -2(x^2 + 3) \] Distributing the -2 gives: \[ f(x^2 + 3) = -2x^2 - 6 \] Thus, we can write: \[ f(g(x)) = -2x^2 - 6 \] To fill in the blanks: \( \left.f(g(x))= -2 x^{2} - 6 \right] \)
