The given functions are:
[tex]\begin{gathered} f(x)=5x-3 \\ g(x)=3x^2+6x+4 \end{gathered}[/tex]
To solve for f(g(6)), first we need to find g(6):
[tex]\begin{gathered} g(6)=3\cdot(6)^2+6(6)+4 \\ g(6)=3\cdot36+36+4 \\ g(6)=108+36+4 \\ g(6)=148 \end{gathered}[/tex]
So, f(g(6))=f(148), now find f(148):
[tex]\begin{gathered} f(148)=5\cdot148-3 \\ f(148)=740-3 \\ f(148)=737 \end{gathered}[/tex]
The answer is f(g(6))=737
b. Find f(f(2)).
Start finding f(2):
[tex]\begin{gathered} f(2)=5\cdot2-3 \\ f(2)=10-3 \\ f(2)=7 \end{gathered}[/tex]
Now, f(f(2))=f(7), solve for f(7):
[tex]\begin{gathered} f(7)=5\cdot7-3 \\ f(7)=35-3 \\ f(7)=32 \end{gathered}[/tex]
The answer is f(f(2))=32
