Range of the function $f(x)=\cos^{-1}(-\

CUET Preparation Today

Start Free Mocks

Home Questions 3MYMW93HPP

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Inverse Trigonometric Functions

Question:

Range of the function $f(x)=\cos^{-1}(-\{x\})$, where {.} is fractional part function is:

Options:

$(\frac{π}{2},π)$

$(\frac{π}{2},π]$

$[\frac{π}{2},π)$

$(0,\frac{π}{2}]$

Correct Answer:

$[\frac{π}{2},π)$

Explanation:

$y=\cos^{-1}(-\{x\})$ As {x} ∈ [0, 1) $⇒\frac{π}{2}≤\cos^{-1}(-\{x\})<π$

$⇒y∈[\frac{π}{2},π)$