Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 3

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Let $A = \{4, 5, 7\}$ and $B = \{2, 4, 6\}$ be two sets and let a relation $R$ be a relation from $A$ to $B$ is defined by $R : \{(x, y) : x < y, x \in A, y \in B\}$ . Then, the difference between the sum of elements of the domain and the range of $R$ is

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Important Questions on Relations and Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 5

The largest set of real values of

x

for which

f (x) = \sqrt{(x + 2) (5 - x)} - \frac{1}{\sqrt{x^{2} - 4}}

is a real function is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 6

The domain of a function

f (x) = \frac{x^{2} + 1}{\ln (x^{2} + 1)}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 7

The domain of definition of the function

f (x) = \log_{3 / 2} \log_{1 / 2} \log_{π} \log_{π / 4} x

is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 8

The domain of a

\log_{[x + 1]} (x^{2} - 1)

, where

[]

represents the greatest integer function, is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 9

The domain of the function

f (x) = \sqrt{x - \sqrt{1 - x^{2}}}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 10

The range of the expression

2^{x} + 2^{- x} + 3^{x} + 3^{- x}

for

x \in R

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 11

The range of the function

y = f (x)

if

{(34)}^{x} + {(34)}^{y} = 34

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 2 - Relations and Functions>Assignment>Q 12

If

f (x)

is a polynomial function of the second degree such that

f (- 3) = 6, f (0) = 6

and

f (2) = 11

, then the graph of the function,

f (x)

cuts the ordinate

x = 1

at the point