(19) Determine whether the following functions are injective, surjective, both, or neither. (a) f: RR defined by f(x) = eª. (b) g: Q→ R defined by g(x) = x³. (c) h: (0, ∞) → (0, 1] defined by h(x) = z²+1 (d) k: [0, ∞) → [7, ∞) defined by k(x) = x² + n.

Q: Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well %3D defined.

A: we need to prove homomorphism

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