5.6.15. Let f: A → B be an arbitrary function. (a) Prove that if f is a bijection (and hence invertible), then f-'(f(x)) = x for all æ E A, and f(f-'(x)) = x for all x E B. (b) Conversely, show that if there is a function g: B → A, satisfying g(f(x)) = x for all x € A, and f(g(x)) = x for all x E B, then f is a bijection, and f = g.
5.6.15. Let f: A → B be an arbitrary function. (a) Prove that if f is a bijection (and hence invertible), then f-'(f(x)) = x for all æ E A, and f(f-'(x)) = x for all x E B. (b) Conversely, show that if there is a function g: B → A, satisfying g(f(x)) = x for all x € A, and f(g(x)) = x for all x E B, then f is a bijection, and f = g.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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