if f(x) = 2x^2+4 and g(x)=x-3 which number satisfies f(x)= (f o g)(x)

Question

A) 3/2
B) 3/4
C) 5
D) 4
I am positive that answer A is correct, i just cant get the work to prove it, i can disprove all other answers and my teacher has assured me i am on the right track, he wants work proving answer A is correct and i have tried many different options such as substitution and even plugging in the variable to solve and i cant seem to do it right at all, i get incorrect and answers that don't make sense, i would really appreciate the help because i truly don't understand

Answer 1

(f◦g)(x) = f(g(x))

Since f(x) = 2x^2+4,
f(g) = 2g^2+4 = 2(x-3)^2+4

So, we want

f(x) = (f◦g)(x)
2x^2+4 = 2(x-3)^2 + 4
x^2 = (x-3)^2
x^2 = x^2-6x+9
0 = -6x+9
x = 3/2