JEE MATHEMATICS MCQ: FUNCTIONS

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A relation

R

is defined in the set

Z

of integers as follows

(x, y) \in R

iff

x^2+y^2=9

. Which of the following is false?

View answer and explanation

Correct option: D

None of the above

Option D (None of the above) is correct because the relation R, defined by

x^2 + y^2 = 9

, includes the pairs (0, 3), (0, -3), (3, 0), and (-3, 0). The domain and range are both {-3, 0, 3}, so all the statements are true, making "None of the above" the correct answer.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains