CHAP. 3] FUNCTIONS AND ALGORITHMS 69
3.34. f−^1 (x)=(x+ 7 )/ 3
3.35. (a) 425631; (b) 416253; (c) 534261; (d) 415623;
(e) 453261.
3.40. (a)A 2 ; (b)A 7 ; (c)Arwhereris the smallest inte-
ger inJ; (d)Aswheresis the largest integer inJ;
(e)Arwhereris the smallest integer inK; (f) Ø.
3.41. (i)D 14 ; (ii)D 24 ; (iii)D 12 (iv)D 3.
3.43. (a) 5; (b) 2^5 =32; (c) 0.
3.44. (a) 5^4 =625; (b)sr; (c) 2^16 =65 536; (d) 2.
3.47. (a) 13,−1, 34; (b) 14, 0, 34.3.48. (a) 5; (b) 0; (c) 2; (d) 6− 5 =1; (e) 11− 5 =6.
3.49. (a) 30; (b) 48; (c) 6; (d) 870.
3.50. (a) 4; (b) 3; (c)−2.
3.51. L( 25 )=4. Each timenis divided by 2, the value ofL
is increased by 1. HenceLis the greatest integer such
that 2L<N. ThusL(n)=log 2 n.
3.52. Q( 2 , 7 )=5,Q( 5 , 3 )=10,Q( 15 , 2 )=42.
3.53. Hint: LetPkdenote the set of polynomialsp(x)such
thatm ≤kand each|ai|≤k.Pkis finite and
P=∪kPk.