Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 37

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The domain of $f (x)$ such that the $f (x) = \frac{[x + \frac{1}{2}]}{[x - \frac{1}{2}]}$ is prime is $[x_{1}, x_{2}),$ then the value of $2 (x_{1}^{2} + x_{2}^{2}) .$ [Where $[.]$ denotes greatest integer function less than or equal to $x]$

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Important Questions on Functions

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 42

If

f (x) = {ax}^{7} + {bx}^{3} + cx - 5; a, b, c

are real constants and

f (- 7) = 7

, then the maximum value of

|f (7) + 17 \cos x|

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 43

Number of solutions of the equation

e^{- \sin^{2} x} = \tan 2 x

in

[0, 10 π]

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 44

Let

f (x) = ([a]^{2} - 5 [a] + 4) x^{3} - (6 {a}^{2} - 5 {a} + 1) x - (tanx) sgn (x)

be an even function

\forall x \in R,

then the sum of all possible values of

' 3 a'

is (where [.] denotes G.I. F and

{\cdot}

fractional part functional part function)

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 45

Let

f

be a one-one function with domain

\{21, 22, 23\}

and range

\{x, y, z\}

. It is given that exactly one of the following statements is true and the remaining two are false.

f (21) = x

; f (22) \neq x; f (23) \neq y .

Then

f^{- 1} (x)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 47

The number of real solutions of equation

\sqrt{1 + \cos 2 x} = \sqrt{2} \sin^{- 1} (\sin x), - 10 π \leq x \leq 10 π

is/are

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 48

f (x) = \sin l n (\frac{\sqrt{4 - x^{2}}}{1 - x}),

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 49

D

is domain and

R

is the range of

f (x) = \sqrt{x - 1} + 2 \sqrt{3 - x},

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 50

Let $D \equiv [- 1, 1]$ is the domain of the following functions, the state which of them are injective.