(a) Explain why the function f(x) = e^x^2 is not injective (one-to-one) on its natural domain. (b) Find the largest possible domain A, where all elements of A are non-negative and f : A → R, f(x) = e^x^2 is injective. (c) Find a codomain B such that f : A → B, f(x) = e^x^2 is surjective. (d) Show that g : B → A, g(x) = √lnx is the inverse of f. Why is f^−1(x) 6 ≠ −√lnx?

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