### Onto Functions

How many onto functions can be defined from the set A = {1, 2, 3, 4} to {a, b, c}?

- 81
- 79
- 36
- 45

**Correct Answer**Choice (C).

36 Correct answer- Explanatory Answer
- Surjective Functions
- Hard

### Quadratic Expressions

Find the maximum value of f(x); if f(x) is defined as the Min {-(x – 1)

^{2}+ 2, (x – 2)^{2}+ 1}- 1
- 2
- 0
- 3

**Correct Answer**Choice (B).

2 Correct answer- Explanatory Answer
- Maximum and Minimum
- Medium

### Compound functions

Consider functions f(x) = x

^{2}+ 2x, g(x) = and h(x) = g(f(x)). What are the domain and range of h(x)?**Correct Answer**Domain: ( -∞, +∞), Range -[0, ∞] Correct answer- Explanatory Answer
- Compound functions
- Medium

### Greatest Integer Function

[x] = greatest integer less than or equal to x. If x lies between 3 and 5, 5 inclusive, what is the probability that [x

^{2}] = [x]^{2}?- Roughly 0.64
- Roughly 0.5
- Roughly 0.14
- Roughly 0.36

**Correct Answer**Choice (C).

Roughly 0.14 Correct answer- Explanatory Answer
- Greatest Integer Function
- Hard

### Domain and Range

Give the domain and range of the following functions:

- f(x) = x
^{2}+ 1 - g(x) = log(x + 1)
- h(x) = 2
^{x} - f(x) = 1/(x+1)
- p(x) = |x + 1|
- q(x) = [2x], where [x] gives the greatest integer less than or equal to x

**Correct Answer**Correct answer- Explanatory Answer
- Domain and Range
- Medium

- f(x) = x
### Domain and Range

How many elements are present in the domain of

^{9–x}C_{x+1}?- 5
- 6
- 4
- 7

**Correct Answer**Choice (B).

6 Correct answer- Explanatory Answer
- Domain and Range
- Medium

### Functions - Unconventional Question

f(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?

- 1/3
- 1/9
- 9
- 6

**Correct Answer**Choice (B).

1/9 Correct answer- Explanatory Answer
- Unconventional Question
- Medium

### Functions - Value of p - q

If f(x – 3) = 2x

^{3 }+ p – qx and f(x^{2 }– 4) = x^{2 }– 8q + 6p, then what is the value of p – q?- 5
- 10
- 6
- Cannot determine

**Correct Answer**Choice (B).

10 Correct answer- Explanatory Answer
- Value of p - q
- Medium

### Functions - Value of a

Given that x is real and f(x) = f(x + 1) + f(x – 1). Determine the value of ‘a’ that will satisfy f(x) + f(x + a) = 0?

- -1
- -2
- 1
- 3

**Correct Answer**Choice (D).

3 Correct answer- Explanatory Answer
- Value of a
- Medium

### Function of a function

x is a real number such that f(x) = 1/x when x > 0 and f(x) = 1/(x + 1) otherwise. Also f

^{n}(x) = f(f^{n - 1 }(x)). What is f(3) + f^{2}(-3) + f^{3}(3) + f^{4}(-3)?- -2/3
- 14/3
- 0
- 3

**Correct Answer**Choice (B).

14/3 Correct answer- Explanatory Answer
- Function of a function
- Medium

### Identical Functions

Which of the following functions are identical? f(x) =

g(x) = (√x)^{2}

h(x) = x

- f(x) and g(x)
- f(x) and h(x)
- All 3 are identical
- None of these are identical

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Domain of a function
- Easy

### Function of a function

The value of fogoh(9) could be, if

f(x) =

g(x) =

h(x) = √x

- 3
- -5
- None of these

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Function of a function
- Medium

### Function of a function

For this question, assume the following operators: A*B = A

^{2}- B^{2}

A-B =

A+B = A * B

= A+B

Which of the following expression would yield the result as x subtracted by y?

- (x*y)-(x+5)
- ()*(x-y)
- (x*y) - ()
- (x+y)*(x-y)

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Function of a function
- Hard

### Domain of Function

Find the domain of: + √(x+1)

- (-∞,9)
- [-1,9)
- [-1,9) excluding 0
- (-1,9)

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Domain of Function
- Hard

### Value of a Sequence

If [X] – Greatest integer less than or equal to x. Find the value of

[√1] + [√2] + [√3] +……………………………………………………+ [√100]

- 615
- 625
- 5050
- 505

**Correct Answer**Choice (B).

Correct answer- Explanatory Answer
- Greatest Integer Function
- Medium

### Greatest Integer Function

Find the value of x for which x[x] = 39

- 6.244
- 6.2
- 6.3
- 6.5

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Greatest Integer Function
- Medium

### Greatest Integer Function

Find the value of x for which x[x] = 15

- 3.5
- 5
- 6.1
- None of these

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Greatest Integer Function
- Medium

### Composite Function

If , then which of the following is correct?

- f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
- f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
- f(f(g(f(x)))) = g(g(f(g(x))))
- f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Composite Functions
- Hard

### Invertible Functions

If . Find the value of x for which f(x) = f

^{-1}(x)?

- -3
- 2
- Both A and B
- None of these

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Invertible Functions
- Medium

### Minimum Value of f(x)

If f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+3t|, where x is an integer and t is a positive integer, find the minimum value of f(x) when t = 6

- 63
- 36
- 30
- 25

**Correct Answer**Choice (B).

Correct answer- Explanatory Answer
- Minimum Value
- Hard

### Minimum Value of f(x)

In the previous question if t = 7, for how many values of x, f(x) will be minimum?

- 1
- 2
- 4
- 8

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Minimum Value
- Hard

### Value of f(x)

If , for all x ≥ 0 and f(x) is a positive-valued function and f(6) = 81, f(2) = 4, find the value of f(4).

- 8
- 18
- 25
- 28

**Correct Answer**Choice (B).

Correct answer- Explanatory Answer
- Value of function
- Medium

- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion

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