\(f(x)=x^2+2x+3\)
\(g(x)=\frac{x+4}{3}\)
\(f(g(x))=(\frac{x+4}{3})^2+2(\frac{x+4}{3})+3\)
\(f(g(x))=\frac{x^2+8x+16}{9}+\frac{2x+8}{3}+3\)
\(f(g(2))=\frac{2^2+8(2)+16}{9}+\frac{2(2)+8}{3}+3\)
\(f(g(2))+\frac{4+16+16}{9}+\frac{4+8}{3}+3\)
\(f(g(2))=\frac{36}{9}+\frac{12}{3}+3\)
\(f(g(2))=4+4+3\)
\(f(g(2)=11\)
Check:
g(2)=(2+4)/3=2
f(2)=2^2+2(2)+3=4+4+3=11 Checks.
