Given the functions:
[tex]\begin{gathered} f(x)=x^2-4x-9 \\ g(x)=-3x-5 \end{gathered}[/tex]
We need to find the function f(g(x)
So, every variable for x in the function f(x) will be substituted with g(x) as follows:
[tex]f(g(x))=(-3x-5)^2-4\cdot(-3x-5)-9[/tex]
Now, we will simplify the expression:
[tex]\begin{gathered} f(g(x))=9x^2+30x+25+12x+20+9 \\ \\ f(g(x))=9x^2+42x+54 \end{gathered}[/tex]
So, the answer will be:
[tex]f(g(x))=9x^2+42x+54[/tex]
