8. Determine which of the following functions are onto.(a) g1:{1,2, 3, 4, 5} → {a, b, c, d, e}; 91(1) = b, g1(2) = b, g1(3) = b, 91(4) = a, g1(5) = d(b) g2: {1, 2, 3, 4, 5} → {a, b, c, d, e}; 92(1) = d, g2(2) = b, g2(3) = e, 92(4) = a, g2(5) = cS (n + 1)/2 if n is oddif n is even(c) g3:N → N; g3(n) ={n/2sn+1 if n is oddIn -1 if n is even(d) g4:N + N; 94(n)

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8. Determine which of the following functions are onto. (a) g1:{1,2, 3, 4, 5} → {a,b, c, d, e}; g1(1) = b, g1(2) = b, g1 (3) = b, g1(4) = a, 91(5) = d (b) g2:{1,2,3, 4, 5} → {a,b, c, d,e}; 92(1) = d, g2(2) = b, g2(3) = e, 92(4): S (n + 1)/2 if n is odd if n is even = a, 92(5) = c (c) g3:N→ N; 93(n) [n/2

8. Determine which of the following functions are onto. (a) g1:{1,2, 3, 4, 5} → {a,b, c, d, e}; g1(1) = b, g1(2) = b, g1 (3) = b, g1(4) = a, 91(5) = d (b) g2:{1,2,3, 4, 5} → {a,b, c, d,e}; 92(1) = d, g2(2) = b, g2(3) = e, 92(4): S (n + 1)/2 if n is odd if n is even = a, 92(5) = c (c) g3:N→ N; 93(n) [n/2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

8. Determine which of the following functions are onto.
(a) g1:{1,2, 3, 4, 5} → {a, b, c, d, e}; 91(1) = b, g1(2) = b, g1(3) = b, 91(4) = a, g1(5) = d
(b) g2: {1, 2, 3, 4, 5} → {a, b, c, d, e}; 92(1) = d, g2(2) = b, g2(3) = e, 92(4) = a, g2(5) = c
S (n + 1)/2 if n is odd
if n is even
(c) g3:N → N; g3(n) =
{n/2
sn+1 if n is odd
In -1 if n is even
(d) g4:N + N; 94(n)

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