The domain of definition of $ cos^{-1}(2

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Inverse Trigonometric Functions

Question:

The domain of definition of $ cos^{-1}(2x-1),$ is

Options:

[-1,1]

[0,1]

[-1,0]

[0,2]

Correct Answer:

[0,1]

Explanation:

The domain of $cos^{-1}x$ is [-1,1]. So, the domain of $cos^{-1}(2x-1)$ is the set of all value of satisfying

$-1 ≤ 2x-1 ≤ 1 ⇒ 0 ≤2x ≤2 ⇒ 0 ≤x ≤1$

Hence, the domain of $cos^{-1}(2x-1) $ is [0,1].