JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

[x]

and

\{x\}

denote the integral part and fractional part of

x

, respectively. Then the number of solutions of the equation

4\{x\}=x+[x]

View answer and explanation

Correct option: B

The correct answer is B (2) because there are two solutions to the equation

4\{x\}=x+[x]

, which are

x=0

and

x=5/3

, found by analyzing the properties of the fractional and integral parts of x.

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

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

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

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

f: R \rightarrow R

f(x)=x^4

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

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