# Relations and Functions

### Let f(x) = min{2x^2, 52 − 5x}, where x is any positive real number

Let f(x) = min{2x2, 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is

### If f(x + 2) = f(x) + f(x + 1) for all positive integers x

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

### The domain of sin-1[log3(x/3)] is

The domain of sin-1[log3(x/3)] is

1. [-9, -1]
2. [-9, 1]
3. [-1,9]
4. [1, 9]

### Let W denote the words in the English dictionary

Let W denote the words in the English dictionary. Define the relation R by:

R = {(x, y) ε W × W | the words x and y have at least one letter in common}. Then R is

1. reflexive, symmetric and not transitive
2. reflexive, symmetric and transitive
3. not reflexive, symmetric and transitive
4. reflexive, not symmetric and transitive

### A function is matched below against an interval

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

1. (-∞,1/3] ; 3x2 - 2x + 1
2. [2,∞) ; 2x3 - 3x2 -12x + 6
3. (-∞,∞) ; x3 - 3x2 + 3x + 3
4. (-∞,-4] ; x3 + 6x2 + 6

### The domain of the function f(x) = 1/√(|x| - x) is

The domain of the function f(x) = 1/√(|x| - x) is

1. (0,∞)
2. (-∞,0)
3. (-∞,∞)
4. (-∞,∞) - {0}

### The function f(x) = log (x + √(x^2 +1)), is

The function f(x) = log (x + √(x2 +1)) is

1. an even function
2. an odd function
3. neither an even nor an odd function
4. a periodic function

### Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

1. not symmetric
2. transitive
3. reflexive
4. a function

### If a ϵ R and the equation -3(x - [x])^2 + 2(x - [x]) + a^2 = 0 has no integral solution

If a ϵ R and the equation -3(x - [x])2 + 2(x - [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

1. (-1, 0) U (0, 1)
2. (-2, -1)
3. (1, 2)
4. (-∞, -2) U (2, ∞)

### For real x, let f(x) = x^3 + 5x + 1, then

For real x, let f(x) = x3 + 5x + 1, then

1. f is one-one and onto R
2. f is onto R but not one-one
3. f is neither one-one nor onto R
4. f is one-one but not onto R

### A function f from the set of natural numbers to integers

A function f from the set of natural numbers to integers defined by

f(n) = (n-1)/2, when n is odd

f(n) = -n/2, when n is even

1. one-­one and onto both
2. one-­one and but not onto
3. neither one-­one nor onto
4. onto but not one-­one