The domain of definition of f ( x ) = 1 - | x | 2 - | x | is

( - ∞ , - 2 ) ∪ [ - 1 , 1 ] ∪ ( 2 , ∞ )

The domain of the function f x = log 3 + x x 2 - 1 is

- 3 , - 2 ∪ - 2 , - 1 ∪ 1 , ∞

[ - 3 , - 2 ) ∪ - 2 , - 1 ∪ 1 , ∞

The domain of the definition of the function f x = 1 4 - x 2 + l o g 10 x 3 - x is:

- 2 , - 1 ∪ - 1 , 0 ∪ 2 , ∞

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Solution of $|1 + \frac{3}{x}| > 2$ is

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Important Questions on Linear Inequalities

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of the function

f (x) = \sqrt{\frac{1}{|x - 2| - (x - 2)}}

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Let

f : (1, 3) \to R

be a function defined by

f (x) = \frac{x [x]}{1 + x^{2}},

where

[x]

denotes the greatest integer

\leq x .

Then the range of

f

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of the function $f : R \to R$ defined by $f (x) = \sqrt{x^{2} - 7 x + 12}$ is

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

\frac{x - P}{x^{2} - 3 x + 2}

takes all real values for

x \in ℝ,

then the range of

P

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The number of solutions of the equation

\log_{4} (x - 1) = \log_{2} (x - 3)

is ______.

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The number of non-constant functions

f

from

X = {0, 1, 2}

Y = {1, 2, 3, 4, 5, 6, 7, 8}

such that

f (i) \leq f (j)

for

i, j \in X

and

i < j

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Let

f : [2, \infty) \to R

be the function defined by

f (x) = x^{2} - 4 x + 5

, then the range

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The range of the function

f (x) = \frac{2 + x}{2 - x}, x \neq 2

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

4^{x} - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2 x - 1}

then value of

x

is equal to

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The range of the polynomial

P (x) = 4 x^{3} - 3 x

x

varies over the interval

(- \frac{1}{2}, \frac{1}{2})

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Let

D = \{x \in ℝ : f (x) = \sqrt{\frac{x - | x |}{x - [x]}}

is defined

}

and

C

be the range of the real function

g (x) = \frac{2 x}{4 + x^{2}} .

Then

D \cap C =

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

g

is the inverse of a function

f

and

f^{'} (x) = \frac{1}{1 + x^{5}},

then

g^{'} (x)

is equal to

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of

f (x) = \sqrt{(\frac{1}{\sqrt{x}} - \sqrt{(x + 1)})}

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following statements -
(i) Relation is a special case of a function.
(ii) Function is a special case of a relation.
(iii) Both relation and function are same.

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of definition of

f (x) = \sqrt{\frac{1 - | x |}{2 - | x |}}

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

A

is a set having

6

distinct elements. The number of distinct functions from

A

A

which are not bijections is

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of the function

f (x) = \log_{3 + x} (x^{2} - 1)

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The domain of the definition of the function

f (x) = \frac{1}{4 - x^{2}} + {l o g}_{10} (x^{3} - x)

is:

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

For

x \in R,

Let

[x]

denotes the greatest integer

\leq x,

then the sum of the series

[- \frac{1}{3}] + [- \frac{1}{3} - \frac{1}{100}] + [- \frac{1}{3} - \frac{2}{100}] + . . . . . + [- \frac{1}{3} - \frac{99}{100}]

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The function

f : N \to I

defined by

f (x) = x - 5 [\frac{x}{5}]

, where

N

is the set of natural numbers and

[x]

denotes the greatest integer less than or equal to

x

, is:

Solution of 1+3x>2 is

Important Questions on Linear Inequalities

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Solution of $|1 + \frac{3}{x}| > 2$ is