Natural isomorphisms via pullbacks

Exercise 1.3.23. Let \(f,g\colon C \to D\) be two functors of \(\infty \)-categories, regarded as objects of \(\Fun (C,D)\). We may define a new \(\infty \)-category \((f \cong g)\) via the following pullback square:

Show that every natural isomorphism \(\alpha \colon f \cong g\) defines an object of \((f \cong g)\). Conversely, show that every object of \((f \cong g)\) defines a natural isomorphism \(\alpha \colon f \cong g\).