Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 1

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Let $f : R \to [1, \infty)$ be defined as $f (x) = \log_{10} (\sqrt{3 x^{2} - 4 x + k + 1} + 10) .$ If $f (x)$ is surjective, then:

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Important Questions on Functions

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 2

Let

f : (- \infty, 0] \to [1, \infty)

be defined as

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

then

f (x)

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 3

Let

A

be a non-empty set of real numbers and

f : A \to A

be such that

f (f (x)) = x, \forall x \in R

Then

f (x)

is:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 4

f : R \to R

defined by

f (x) = \frac{1}{2} x | x | + \cos x + 1

is:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 5

Let

f : R \to R,

f (x) = \{\begin{cases} 2 x + α^{2} & x \geq 2 \\ \frac{α x}{2} + 10 & x < 2 \end{cases}

is onto function, then

α

belongs to:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 6

Let

f : R \to (0, \frac{2 π}{3}]

defined as

f (x) = \cot^{- 1} (x^{2} - 4 x + α)

. Then the smallest integral value of

α

such that

f (x)

is into function, is:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 7

Let

f : R^{+} \to \{- 1, 0, 1\}

be defined by

f (x) = sgn (x - x^{4} + x^{7} - x^{8} - 1)

where

sgn

denotes signum function. Then

f (x)

is.

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 8

Which of the following statements are incorrect?

$I$ . If $f (x)$ and $g (x)$ are one-one, then $f (x) + g (x)$ is also one-one.

$II$ . If $f (x)$ and $g (x)$ are one-one, then $f (x) \cdot g (x)$ is also one-one.

$III$ . If $f (x)$ is odd, then it is necessarily one-one.

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 1 - Functions>DPP>Q 9

Which of the following functions is one-one?