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 = 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 , + ∞

Let f x = sin π 6 sin π 2 sin x , for all x ∈ R and g x = π 2 sin x , for all x ∈ R . Let f o g x denote f g x and g o f x denote g f x . Then which of the following is (are) true?

lim x → 0 f ( x ) g ( x ) = π 6

There is an x ∈ R such that g o f x = 1

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

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

EASY

Earn 100

In which of the following representation, we may have a finite number of the exact values of the dependent variable corresponding to the independent variable?

$A .$ Analytical representation

$B .$ Graphical representation

$C .$ Tabular representation

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Important Questions on Sets, Relations and Functions

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

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>Functions

Domain of

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

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

. Then

f^{- 1} (x) =

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

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>Functions

The range of the function

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Functions

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>Functions

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

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

The range of the polynomial

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

x

varies over the interval

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

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Functions

The domain of the function

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

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

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>Functions

y = 4 + 9 \sin 5 x

then which holds good?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

The domain of the function

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

The range of the function

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

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

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

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

f

be a continuous function defined on

[0, 1]

such that

\int_{0}^{1} f^{2} (x) d x = {(\int_{0}^{1} f (x) d x)}^{2}

. Then the range of

f

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

f (x) = \sin (\frac{π}{6} \sin (\frac{π}{2} \sin x))

, for all

x \in R

and

g (x) = \frac{π}{2} \sin x

, for all

x \in R

. Let

(f o g) (x)

denote

f (g (x))

and

(g o f) (x)

denote

g (f (x))

. Then which of the following is (are) true?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

f : (- 1, 1) \to (- 1, 1)

be continuous,

f (x) = f (x^{2})

for all

x \in (- 1, 1)

and

f (0) = \frac{1}{2}

,

then the value of

4 f (\frac{1}{4})

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Functions

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>Functions

The domain of definition of

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

f : [2, \infty) \to R

be the function defined by

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

, then the range

In which of the following representation, we may have a finite number of the exact values of the dependent variable corresponding to the independent variable? A. Analytical representation B. Graphical representation C. Tabular representation

Important Questions on Sets, Relations and Functions

Learn and Prepare for any exam you want !

In which of the following representation, we may have a finite number of the exact values of the dependent variable corresponding to the independent variable?

$A .$ Analytical representation

$B .$ Graphical representation

$C .$ Tabular representation