JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

[.] denotes greatest integer function and

\{\}

denotes fractions part function. If A,B denote the domain and the range of the function

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

and

g(x)=\sqrt{\{x\}^2-2\{x\}}

respectively, then sum of all integers in

\mathrm{A} \cup \mathrm{B}

View answer and explanation

Correct option: A

Option A (3) is correct because the domain of f(x) is [0,3) and the range of g(x) is an empty set, so the union contains integers 0, 1, and 2, summing to 3.

More Questions from FUNCTIONS

Practice All Chapter MCQs →

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