Initial work

CS1029/practical-2023-10-20/functions

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+1. a) f(x) is undefined for x = 0
+   b) f(x) is complex for x < 0
+   c) multivalued
+
+2. a) multivalued
+   b) It is
+   c) undefined at x = 2
+
+3. a) Z >= 0, {0..9}
+   b) 0.. -> 1..?
+   c) All bit strings -> N
+   d) All bit strings -> N
+   e) (Z^+)^2 -> Z^+
+   f) (Z^+)^2 -> Z^+
+
+4. a) 1 b) 2 c) -1 d) 0 e) 2 f) 3 g) 0 h) 2
+5. a) 1 b) 0 c) 0 d) -1 e) 3 f) -1 g) 2 h) 1
+
+8. a) 6 b) 24 c) 120 d) 3_628_800
+
+10. a)y b)n c)n
+11. {a}
+
+12. a) y b) n c) n d) n
+13. a) y b) n) c) y) d) n
+
+14. ynyy
+
+15. a) everyone has a phone number (phone numbers should already be uniquie)
+    b) None (student ids should already be unique)
+	c) Every student gets a unique grade
+	d) no two people come from the same town
+
+16. a) the set of phone numbers
+    b) the set of student ids
+	c) 1..100
+	d) all towns
+
+17. ynnn
+18. a) { 1 }
+    b) { -1, 1, 5, 9, 15 }
+	c) { 0, 1, 2 }
+	d) { 0, 1, 2 }
+
+19. f.g = x^2 + 4x + 5, g.f = x^2 + 3
+20. f + g = x^2 + x + 3
+    fg = x^3 + 2x^2 + x + 2
+
+21. f^-1 doesn't exist, assuming f^-1(x) = +sqrt(x)
+   a) { 1 }
+   b) { x | 0 < x < 1 }
+   c) { x | x > 2 }