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

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

The domain of the function f x = 1 log 10 1 - x + x + 2 is

- 3 , - 2 . 5 ∪ - 2 . 5 , - 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 the function f x = log 3 + x x 2 - 1 is

- 3 , - 2 ∪ - 2 , - 1 ∪ 1 , ∞

[ - 3 , - 2 ) ∪ - 2 , - 1 ∪ 1 , ∞

HARD

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The domain of the function $\sin^{-1} (\log_{2} \frac{x^{2}}{2})$ is

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Important Questions on Functions

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

The range of the function

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

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

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 =

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of definition of

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

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of function

y = \sqrt{x - 2} + \sqrt{1 - x}

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

Let

f : [2, \infty) \to R

be the function defined by

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

, then the range

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the function

f (x) = \frac{\sin^{- 1} (x - 3)}{\sqrt{9 - x^{2}}}

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of

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

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

Range of the function

f (x) = {}^{7 - x}P_{x - 3},

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

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

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the function

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

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the function

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

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the definition of the function

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

is:

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the function

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

EASY

Mathematics>Differential Calculus>Functions>Basics of Functions

The domain of the function

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

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

Let

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

(where

[.]

denotes the greatest integer function), then the range of

f (x)

MEDIUM

Mathematics>Differential Calculus>Functions>Basics of 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:

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

Let

[x]

denote the greatest integer

\leq x

, where

x \in R

. If the domain of the real valued function

f (x) = \sqrt{\frac{|[x]| - 2}{|[x]| - 3}}

(- \infty, a) \cup [b, c) \cup [4, \infty), a < b < c

, then the value of

a + b + c

is:

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

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

takes all real values for

x \in ℝ,

then the range of

P

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

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

HARD

Mathematics>Differential Calculus>Functions>Basics of Functions

The range of the polynomial

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

x

varies over the interval

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

The domain of the function sin-1⁡log2⁡x22 is

Important Questions on Functions

Learn and Prepare for any exam you want !

The domain of the function $\sin^{-1} (\log_{2} \frac{x^{2}}{2})$ is