Question

Theorem 7.7. Let f : A ? B be a function. (1) If f has an inverse function, then f is a bijection. (2) If f is a bijection, then f has an inverse function.

          Theorem 7.7. Let f : A ? B be a function.
(1) If f has an inverse function, then f is a bijection.
(2) If f is a bijection, then f has an inverse function.

Added by Corey M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/06/2023

Step 1

Proof: Suppose $f: A \to B$ has an inverse function $g: B \to A$. By definition of an inverse function, we have $g(f(a)) = a$ for all $a \in A$ and $f(g(b)) = b$ for all $b \in B$. To show that $f$ is a bijection, we need to show that $f$ is both injective Show more…

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Theorem 7.7. Let f : A → B be a function. (1) If f has an inverse function, then f is a bijection. (2) If f is a bijection, then f has an inverse function.