Unformatted text preview: 9 0 I lies entirely on or below the xaxis.) 1 17. (a) 1 0 g(x) = I(g(xÂ» = I( 1~:zJ = 11= 1 (1 x) = Â£(x). 1x 1 go r(x) = g(r(xÂ» = g(x:'1) = 1. ...L = (x:'l{x = X:: 1 1 = 1x = s(x). x1 1 11Â£ I 9 h r sl Â£ Â£ IÂ· 9 h r s I I 9 Â£ S h r 9 9 Â£ I r s h h h r s Â£ I 9 r r s h 9 Â£ I s s h r I 9 Â£ inverse (b) All these functions have inverses. function 18. (a) 0 Â£ It h fa 14 15 Â£ Â£ It h fa 14 15 It It Â£ 14 15 h fa h h 15 Â£ !4 fa h fa fa !4 15 Â£ h h 14 !4 fa It h 15 Â£ 15 15 h fa 11 Â£ 14 (b) All these functions have inverses. inverse function 19. (a) [BB] log = {(1, 4), (2,3), (3,2), (4, 1), (5, 5)}; 9 0 1= {(1, 5), (2,3), (3,2), (4,4), (5, 1)} Clearly, log =I 9 0 I. (b) 11 = {(1, 2), (2, 1), (3, 5), (4,3), (5, 4)}; g1 = {(1, 3), (2,4), (3, 1), (4,5), (5, 2)} Functions I and 9 have inverses because they are onetoone and onto while h does not have an inverse because it is not onetoone (equally because it is not onto)....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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