Let J₅ = {0, 1, 2, 3, 4}, and define functions f : J₅ → J₅ and g : J₅ → J₅ as follows:
For each x ∈ J₅:
f(x) = (x + 4)² mod 5
g(x) = (x² + 3x + 1) mod 5
Is f = g? Explain:
a) Yes, because both functions yield the same output for every input in J₅.
b) No, because they produce different outputs for some inputs in J₅.
c) Yes, because they are both linear functions.
d) No, because f is quadratic while g is linear.