Functions

Functions as Mappings

A function $f: A \to B$ assigns to each element of $A$ (the domain) exactly one element of $B$ (the codomain). The range (or image) is $f(A) = \{f(a) : a \in A\}$.

Classification

A bijection from $A$ to $B$ implies $|A| = |B|$.

def is_injective(f_dict):
    values = list(f_dict.values())
    return len(values) == len(set(values))

def is_surjective(f_dict, codomain):
    return set(f_dict.values()) == codomain

def is_bijective(f_dict, codomain):
    return is_injective(f_dict) and is_surjective(f_dict, codomain)

f = {1: 'a', 2: 'b', 3: 'c'}
print(is_bijective(f, {'a', 'b', 'c'}))  # True

Composition and Inverse

$(g \circ f)(x) = g(f(x))$. A function $f$ has an inverse $f^{-1}$ if and only if it is bijective.

Your Task

Implement is_injective, is_surjective, and is_bijective as shown above.