Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 56

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A real valued function $f (x)$ satisfies the functional equation $f (x - y) = f (x) f (y) - f (a - x) f (a + y)$ , where ${}^{'}a^{'}$ is a given constant and $f (0) = 1$ , then $f (2 a - x)$ is equal to

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Important Questions on Relation and Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 69

Let

f (x) = \max . \{x^{2}, (1 - x)^{2}, 2 x (1 - x)\}

, where

0 \leq x \leq 1

then

f (\frac{1}{5}) + f (\frac{1}{2}) + f (\frac{1}{\sqrt{2}})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 65

The range of function

f (x) = sgn (\sin x) + sgn (\cos x) + sgn (\tan x), x \neq \frac{(2 n + 1) π}{2}, n \in I

contain integers

a_{1}, a_{2}, a_{3}, a_{4}, \dots

Then

a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + \dots

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 66

Let

A

consists

5

different elements and set

B

consists

4

different elements. Number of mapping which can be defined from set

A

to set

B

which are surjective, is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 67

If the equation

| x - 1 | - | x - 13 | = k

has exactly one solution, then number of integral values of

k

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 68

Let

g (x) = \sin^{2} (\ln x) + \cos^{2} (\ln x)

then sum of least integral value of domain of

g (x)

and the integral values in range of

g (x)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 70

The range of $f (x) = \sqrt{x - 1} + 2 \sqrt{3 - x}$ is $[a, b]$ then $a^{2} + b^{2}$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 3

Let

f : (- 1, \frac{- 1}{\sqrt{3}}) \to B

, be a function defined by

f (x) = \tan^{- 1} \frac{3 x - x^{3}}{1 - 3 x^{2}}

, then

f

is both one-one and onto when

B

is the interval

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 15

Identify the correct statement