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Robert Fischer · Answer 1 · 2023-11-21T02:30:31+0000

Solution:

Given the functions:

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

To find g(f(x)), we substitute the f(x) function into the g(x) function.

Thus, we have

$\begin{gathered} g(f(x))=g((1)/(3)x^2+4) \\ this\text{ gives} \\ 9((1)/(3)x^2+4)-12 \\ open\text{ parentheses,} \\ 9((1)/(3)x^2)+9(4)-12 \\ =3x^2+36-14 \\ \Rightarrow g(f(x))=3x^2+24 \end{gathered}$

Hence, we have

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