Given that f(x)=5x^2 - 3x + 7 and f(g(x)) = 40 - 11x^2 - 8x^4, find all possible values for the sum of the coefficients in the polynomial function g(x). Thank you to anyone who replies :)

Are you sure you have written the equations correctly? g(x) must be of order 2, so its highest order term is ax^{2}. This means we must have 5a^{2} = -8 (because 5a^{2}x^{4} must equal -8x^{4}). This would make 'a' an imaginary number!