Respuesta :

Answer

Explanation

Given:

[tex]\begin{gathered} f(x)=\frac{1}{3}x^2+4 \\ g(x)=9x-12 \end{gathered}[/tex]

To determine the value of g(f(x)), we substitute x with 1/3x^2+4 for g=9x-12:

[tex]\begin{gathered} g(x)=9x-12 \\ g(\frac{1}{3}x^2+4)=9(\frac{1}{3}x^2+4)-12 \\ Simplify \\ =3x^2+36-12 \\ =3x^2+24 \end{gathered}[/tex]

Therefore, the value of g(f(x)) is C:

[tex]\begin{equation*} 3x^2+24 \end{equation*}[/tex]

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