Composition

Let $f(x) = x + 3$ and $g(x) = x^2$. Compute $(g \circ f)(2)$.

If $f : A \to B$ and $g : B \to C$, what are the domain and codomain of $g \circ f$?

Let $f(x) = 3x$ and $g(x) = x - 2$. Compute $(g \circ f)(4) - (f \circ g)(4)$.

Suppose $g \circ f$ is injective. Which of these must be true? (Choose all that apply.)

In Lean, comp_assoc is proved by rfl. What does that tell us?

Finite functions can be stored as dictionaries. Write compose(g, f) returning a dictionary for $g \circ f$ (apply f first!). You may assume every value of f is a key of g.