Relations and Functions

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 S = N \0\. Define a relation R from S to R by : R = \(x, y) : e y = x e ( 25 ), x S, y R \. Then, the sum of all the elements in the range of R is equal to :

1. 32
2. 109
3. 52
4. 53

If the domain of the function 5(18x - x2 - 77) is ( , ) and the domain of the function (x-1) ( 2x2 + 3x - 2x2 - 3x - 4 ) is ( , ), then 2 + 2 + 2 is equal to:

1. 186
2. 179
3. 195
4. 174

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

The number of real solution(s) of the equation x2+3x+2= \|x-3|,|x+2|\ is :

1. 2
2. 3
3. 1
4. 0

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

1. (0, )
2. [1, )
3. R
4. [0, )

The product of all solutions of the equation e5( ex)2+3=x8, x>0, is :

1. e2
2. e
3. e6/5
4. e8/5

Let f(x) = 17 - 5x be a function defined on R. Then the range of the function f(x) is equal to :

1. [ 18, 15 ]
2. [ 17, 16 ]
3. [ 17, 15 ]
4. [ 18, 16 ]