Question

let g(x)=x+2. Find f(x) if f(x) is a quadratic function of the form f(x)=ax^2+bx+c and f(g(x))=2x^2-x+3

Answer 1

Let g(x) = x + 2
f(g(x)) = 2x^2 - x + 3
= 2(x^2 - x/2 + 3/2)
=2 (x^2 + 4x + 4) - 9x - 5
=2 (x+2)^2 - 9(x+5/9)
=2 (x + 2)^2 - 9 (x + 2) +13
f(x) = 2x^2 -9x + 13