Solution:
Given the functions:
[tex]\begin{gathered} f(x)=\frac{1}{3}x^2+4 \\ g(x)=9x-12 \end{gathered}[/tex]
To find g(f(x)), we substitute the f(x) function into the g(x) function.
Thus, we have
[tex]\begin{gathered} g(f(x))=g(\frac{1}{3}x^2+4) \\ this\text{ gives} \\ 9(\frac{1}{3}x^2+4)-12 \\ open\text{ parentheses,} \\ 9(\frac{1}{3}x^2)+9(4)-12 \\ =3x^2+36-14 \\ \Rightarrow g(f(x))=3x^2+24 \end{gathered}[/tex]
Hence, we have
[tex]g(f(x))=3x^2+24[/tex]
