If x ∈ ( a , b ) satisfies the inequality x - 3 x 2 + 3 x + 2 ≥ 1 , then the largest possible value of b - a is

No real valued x satisfies the inequality

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 function f x = 1 log 10 1 - x + x + 2 is

- 3 , - 2 . 5 ∪ - 2 . 5 , - 2

/ f ( x ) = x 3 - 5 x 2 - 8 x 3 is

negative and monotonically increasing for x ∈ - ∞ , 5 - 57 2 and positive and monotonically increasing for x ∈ 5 + 57 2 , + ∞

positive and monotonically increasing for x ∈ - ∞ , 5 - 57 2 and x ∈ 5 + 57 2 , + ∞

negative and monotonically decreasing for x ∈ - ∞ , 5 - 57 2 and x ∈ 5 + 57 2 , + ∞

positive and monotonically increasing for x ∈ - ∞ , 5 - 57 2 and negative and monotonically decreasing for x ∈ 5 + 57 2 , + ∞

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 , ∞

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

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

EASY

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In a liquid limit test, the moisture content at $10$ blows was $70 %$ and that at $100$ blows was $20 %$ . The liquid limit of the soil is.

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Important Questions on Sets, Relations and Functions

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

For

a > b > c > 0

, the minimum value of the function

f (x) = | x - a | + | x - b | + | x - c |

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Domain of

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Let

f (x) = {(x + 2)}^{2} - 2, x \geq - 2

. Then

f^{- 1} (x) =

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Given

f (x) \dots x^{2} + \log_{3} x

and

g (y) \dots 2 y + f (y)

, the value of

g (3)

equals

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The range of the function

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

x \in (a, b)

satisfies the inequality

\frac{x - 3}{x^{2} + 3 x + 2} \geq 1

, then the largest possible value of

b - a

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Let

f : A \to B, g : B \to A

be defined as

f (x) = x^{2} \forall x \in A

and

g (x) = x^{1 / 2} \forall x \in B

f (x)

and

g (x)

are inverse functions to each other when

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of the function

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of the function

f (x) = \frac{1}{\log_{10} (1 - x)} + \sqrt{(x + 2)}

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Let

f (x) = \sqrt{[\sin 2 x] - [\cos 2 x]}

(where

[.]

denotes the greatest integer function), then the range of

f (x)

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

y = 4 + 9 \sin 5 x

then which holds good?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of the function

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The range of the function

f (x) = \frac{1}{2 - \cos 3 x}

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

f (x) = \frac{x^{3} - 5 x^{2} - 8 x}{3}

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of the definition of the function

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

is:

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of the function

f (x) = \frac{\log (x + 5)}{x^{2} + 4 x + 3}

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

In which of the following domains

f (x)

is continuous, where

f (x) = \frac{| x + 2 |}{\tan^{- 1} (x + 2)} ?

(Note:

R

denotes set of real numbers)

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

If the domain of the function

f (x) = \frac{\cos^{- 1} \sqrt{x^{2} - x + 1}}{\sqrt{\sin^{- 1} (\frac{2 x - 1}{2})}}

is the interval

(α, β],

then

α + β

is equal to:

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The domain of definition of

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Let

f : [2, \infty) \to R

be the function defined by

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

, then the range

In a liquid limit test, the moisture content at 10 blows was 70% and that at 100 blows was 20%. The liquid limit of the soil is.

Important Questions on Sets, Relations and Functions

Learn and Prepare for any exam you want !

In a liquid limit test, the moisture content at $10$ blows was $70 %$ and that at $100$ blows was $20 %$ . The liquid limit of the soil is.