Polynomials and functions

Question

if $y_1 = y_2$ then how we can prove that $x_1 = x_2$ in the following polynomial : $${x_1}^3 + 2{x_1}^2 + 1 = {x_2}^3 +2{x_2}^2+1$$

(I want to see weather a relation is a function)

Answer 1

I believe you want to show wheher a function is an injection.

$$f(x)=x^3+2x^2+1=x^2(x+2)+1$$

$$f(0)=1$$ $$f(-2)=1$$