Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 44

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If $F : [1, \infty) \to [2, \infty)$ is given by $f (x) = x + \frac{1}{x},$ then $f^{- 1} (x)$ equals

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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 50

If

f (x + 10) + f (x + 4) = 0

, there

f (x)

is a periodic function with period

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 52

Let

g (x)

be a polynomial function satisfying

g (x) \cdot g (y) = g (x) + g (y) + g (x y) - 2

for all

x, y \in R

and

g (1) \neq 1

. If

g (3) = 10

then

g (5)

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 54

If

f (x) = a (x^{n} + 3); f (1) = 12, f (3) = 36

; then

f (2)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 55

If

f (x + \frac{1}{y}) + f (x - \frac{1}{y}) = 2 f (x) f (\frac{1}{y})

for all

x

,

y \in R - {0}

and

f (0) = \frac{1}{2}

, then

f (4)

is

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

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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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