Final answer:
Two non-equivalent polynomials f(x) = 2x + 3 and g(x) = 2x + 1 satisfy f(0) = g(0) and f(1) = g(1).
Step-by-step explanation:
In order for two polynomials to be non-equivalent, they must have at least one different coefficient in their terms. Let's consider two polynomials: f(x) = 2x + 3 and g(x) = 2x + 1.
For f(0) = g(0), we substitute x = 0 into both polynomials. f(0) = 2(0) + 3 = 3 and g(0) = 2(0) + 1 = 1. Since 3 is not equal to 1, these polynomials are not equivalent.
Similarly, for f(1) = g(1), we substitute x = 1 into both polynomials. f(1) = 2(1) + 3 = 5 and g(1) = 2(1) + 1 = 3. Since 5 is not equal to 3, these polynomials are also not equivalent.
Therefore, f(x) = 2x + 3 and g(x) = 2x + 1 are two non-equivalent polynomials that satisfy f(0) = g(0) and f(1) = g(1).