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)=(x+4)/(3)`

`f(g(x))=((x+4)/(3))^2+2((x+4)/(3))+3`

`f(g(x))=(x^2+8x+16)/(9)+(2x+8)/(3)+3`

`f(g(2))=(2^2+8(2)+16)/(9)+(2(2)+8)/(3)+3`

`f(g(2))+(4+16+16)/(9)+(4+8)/(3)+3`

`f(g(2))=(36)/(9)+(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.