Relations and Functions · Question 13

Let the domains of the functions f(x) = 4 3 7 (8 - 2 (x2 + 4x + 5 ) ) and g(x) = -1 ( 7x + 10x - 2 ) be ( , ) and [ , ], respectively. Then 2 + 2 + 2 + 2 is equal to :

1. 15
2. 13
3. 16
4. 14

If the domain of the function f(x) = e ( 2x-35+4x ) + -1 ( 4+3x2-x ) is [ , ), then 2 + 4 is equal to

1. 4
2. 3
3. 7
4. 5

If the domain of the function f(x) = 7 (1 - 4 (x2 - 9x + 18 ) ) is ( , ) ( , ), then + + + is equal to

1. 17
2. 15
3. 16
4. 18

Let A = \1, 2, 3, , 100\ and R be a relation on A such that R = \(a, b) : a = 2b + 1\. Let (a1, a2), (a2, a3), (a3, a4), , (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to :

1. 6
2. 8
3. 7
4. 5

If the domain of the function f(x) = 1 10 + 3x - x2 + 1 x + |x| is (a, b), then (1 + a)2 + b2 is equal to :

1. 29
2. 30
3. 25
4. 26

Let f : R R be a function defined by f(x) = (2 + 3a)x2 + ( a+2a-1 )x + b, a 1. If f(x + y) = f(x) + f(y) + 1 - 27xy, then the value of 28 i=15|f(i)| is

1. 735
2. 675
3. 715
4. 545