Question

Given that f(x) = x2 + 2x + 3 and g(x) = quantity of x plus four, over three , solve for f(g(x)) when x = 2.

Answer 1

G(2)=(x+4)/3=2 F(2)=x^2+2x+3 4+4+3=11

Answer 2

$f(x)=x^2+2x+3$
$g(x)=\frac{x+4}{3}$
$f(g(x))=(\frac{x+4}{3})^2+2(\frac{x+4}{3})+3$
$f(g(x))=\frac{x^2+8x+16}{9}+\frac{2x+8}{3}+3$
$f(g(2))=\frac{2^2+8(2)+16}{9}+\frac{2(2)+8}{3}+3$
$f(g(2))+\frac{4+16+16}{9}+\frac{4+8}{3}+3$
$f(g(2))=\frac{36}{9}+\frac{12}{3}+3$
$f(g(2))=4+4+3$
$f(g(2)=11$

Check:
g(2)=(2+4)/3=2
f(2)=2^2+2(2)+3=4+4+3=11  Checks.