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 , + ∞

The function f ( x ) = sec log x + 1 + x 2 is

neither an odd nor an even function

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

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

HARD

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Which of the following statement is correct regarding the function given below?

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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

P (x)

be a polynomial with real coefficients such that

P ({s i n}^{2} x) = P ({c o s}^{2} x),

for all

x \in [0, \frac{π}{2}] .

Consider the following statements:

I.

P (x)

is an even function.

II.

P (x)

can be expressed as a polynomial in

{(2 x - 1)}^{2}

III.

P (x)

is a polynomial of even degree. Then

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}

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Functions

The function

f (x) = \sec [\log (x + \sqrt{1 + x^{2}})]

EASY

Mathematics>Algebra>Sets, Relations and Functions>Functions

f : R \to R,

such that

f (x) = \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}},

then

f

HARD

Mathematics>Algebra>Sets, Relations and Functions>Functions

Let

f (x) = a^{x} (a > 0)

be written as

f (x) = f_{1} (x) + f_{2} (x),

where

f_{1} (x)

is an even function and

f_{2} (x)

is an odd function. Then

f_{1} (x + y) + f_{1} (x - y)

equals:

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

Which of the following statement is correct regarding the function given below?

Important Questions on Sets, Relations and Functions

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