Question

Consider these functions:1(0) =[=2 + 4(=) =91 - 12What is the value of gl (x)?

Answer 1

Solution:

Given the functions:

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

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

Thus, we have

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

Hence, we have

$g(f(x))=3x^2+24$