Composite function

Question

Determine the function g when f(x)=x-3 and fg(x)=2x²-4x+7

Answer 1

It appears that g(x) = 2x² -4x +10, because when you form the composite f(g(x)), you're plugging all of g into the "x" in the f(x) = x - 3 expression. So f (g(x)) = (2x² -4x + 10) - 3 = 2x² -4x + 7.