Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 33

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A function $g (x)$ satisfies the following conditions
(i) Domain of $g$ is $(- \infty, \infty)$

(ii) Range of $g$ is $[- 1, 7]$
(iii) $g$ has a period $π$ and
(iv) $g (2) = 3$

Then which of the following may be possible.

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Important Questions on Functions

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 34

The complete solution set of the inequality

{[\cot^{- 1} x]}^{2} - 6 [\cot^{- 1} x] + 9 \leq 0,

where

[.]

denotes greatest integer function, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 35

If $f (x) = \cot^{- 1} x : R^{+} \to (0, \frac{π}{2})$

and $g (x) = 2 x - x^{2} : R \to R .$ Then the range of the function $f (g (x))$ wherever defined is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 36

The domain of the function

y = \sqrt{sinx + cosx} + \sqrt{7 x - x^{2} - 6}

is

[p, \frac{qπ}{4}] \cup [\frac{rπ}{4}, s]

then value of

p + q + r + s

is

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

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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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