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. 2 5 11 33

Answer 1

basically sub g(x) for x in f(x)


`f(g(x))=( g(x))^2+2(g(x))+3`

`f(g(x))=( (x+4)/(3))^2+2( (x+4)/(3))+3`
we don't need to simplify


`f(g(2))=( (2+4)/(3))^2+2( (2+4)/(3))+3`
[tex]f(g(2)))=( \frac{6}{3})^2+2( \frac{6}{3})+3[/tex
[tex]f(g(2)))=(2)^2+2(2)+3[/tex
f(g(2))=4+4+3
f(g(2))=11
answer is 11