Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $\left[\log_2\left(\frac{x}{[x]}\right)\right]≥0$, where [.] denotes the greatest integer function, then

Options:

$x∈(−∞, ∞) ~ [0, 1)$

$x∈(−∞, 0)$

$x∈[1, ∞)$

none of these

Correct Answer:

none of these

Explanation:

$\left[\log_2\left(\frac{x}{[x]}\right)\right]≥0⇒\log_2\left(\frac{x}{[x]}\right)≥0⇒\frac{x}{[x]}≥1⇒\frac{x-[x]}{[x]}≥0⇒\frac{\{x\}}{[x]}≥0$

It implies that ‘x’ is any positive real number greater than or equal to one or ‘x’ is any non zero integer.