EXAMPLE 3.16. The function F: ZxZ Z defined by the formula F (m, n) = 2m + 3n is a function of two variables on the set Z. EXAMPLE 3.17. The function G : ZxZ Z defined by the formula G (m, n) = m +2+n is also a function of two variables on the set Z. EXAMPLE 3.18. The function H: Z, x Z5 –→ {♡, 0} defined by V if m + n is even H(m, n) = %3D O if m +n is odd is a function of two variables on the set Zg. ACTIVITY 3.44. For the above three functions, calculate: (a) F (1,5) (b) F (5,1) (c) G(-3,7) (d) G (3,-7) (e) H (2, 2) (f) H (1,2)

EXAMPLE 3.16. The function F: ZxZ Z defined by the formula F (m, n) = 2m + 3n is a function of two variables on the set Z. EXAMPLE 3.17. The function G : ZxZ Z defined by the formula G (m, n) = m +2+n is also a function of two variables on the set Z. EXAMPLE 3.18. The function H: Z, x Z5 –→ {♡, 0} defined by V if m + n is even H(m, n) = %3D O if m +n is odd is a function of two variables on the set Zg. ACTIVITY 3.44. For the above three functions, calculate: (a) F (1,5) (b) F (5,1) (c) G(-3,7) (d) G (3,-7) (e) H (2, 2) (f) H (1,2)

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

activity 3.44

Junction of two variables on the set X is a function with domain X × X. For the
record, we restate the above as an 'official definition'.
DEFINITION 3.13. Let X and Y be sets. If F: X x X → Y is a function, we
will refer to F as a function of two variables on the set X.
EXAMPLE 3.16. The function F: ZxZ Z defined by the formula F (m, n) =
2m + 3n is a function of two variables on the set Z.
EXAMPLE 3.17. The function G : Z×Z→ Z defined by the formula G (m, n) =
m +2+n is also a function of two variables on the set Z.
EXAMPLE 3.18. The function H: Z, x Z3 {♡, O} defined by
{
♡ if m +n is even
H (m, n) =
♡
ef m +n is odd
is a function of two variables or the set Z.
.
ACTIVITY 3.44. For the above three functions, calculate:
(a) F (1,5)
(b) F (5, 1)
(c) G(-3,7)
(а) g (3, -7)
(e) H(2, 2)
(f) H (1, 2)

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