# hw18 - be given by h x = 3 √ x-1 a Show that f = f-1 b...

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Intro to Abstract Math Homework 18 Fall 2009 Due October 26 Exercise 52. Let f and g be functions from X to Y . Prove that f = g if and only if f ( x ) = g ( x ) for all x X . Exercise 53. Let f : R [ - 4 , ) be given by f ( x ) = ( x +1) 2 - 4 and let g : [ - 4 , ) R be given by g ( x ) = - 1 - 4 + x . a. Compute f g and g f . b. Are f and g inverses? Be sure to justify your answer. Exercise 54. Let f : [0 , 1] [0 , 1] be given by f ( x ) = 1 - x 2 , let g : R R be given by g ( x ) = x 3 + 1 and let h : R R
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Unformatted text preview: be given by h ( x ) = 3 √ x-1. a. Show that f = f-1 . b. Show that g = h-1 . Exercise 55. Let X = R- { 3 } . Deﬁne f : X → R by f ( x ) = x/ ( x-3). a. Show that f is not a bijection. b. Find a set Y ⊆ R so that the function g : X → Y , given by the same formula as f , is a bijection. c. Find g-1 ....
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