Replace the x symbol with x + 3 in the function equation f(x).
[tex]f(x)=2x^2+1,\ g(x)=x+3\\\\f(g(x))=2(x+3)^2+1[/tex]
use (a + b)² = a² + 2ab + b²
[tex]=2(x^2+2(x)(3)+3^2)+1\\\\=2(x^2+6x+9)+1[/tex]
use distributive property: a(b + c) = ab + ac
[tex]=(2)(x^2)+(2)(6x)+(2)(9)+1=2x^2+12x+18+1=2x^2+12x+19[/tex]
Answer: f(g(x)) = 2x² + 12x + 19.
