To find g(f(x)) we need to substitute x = f(x) into g(x), as follows:
[tex]\begin{gathered} g(x)=3x^2 \\ f(x)=5x+3 \\ g(f(x))=3(5x+3)^2 \\ \text{ Expanding the square of a binomial:} \\ g(f(x))=3\lbrack(5x)^2+2(5x)3+3^2\rbrack \\ g(f(x))=3\lbrack25x^2+30x+9\rbrack \\ \text{ Distributing:} \\ g(f(x))=3(25x^2)+3(30x)+3(9) \\ g(f(x))=75x^2+90x+27 \end{gathered}[/tex]
