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Mathematics Question on Inverse Trigonometric Functions

The domain of the function cos−1(2x−1)cos^{-1}(2x - 1) is

A

[0,1][0,1]

B

[−1,1][-1,1]

C

(−1,1)( - 1, 1 )

D

[0,π][0, \pi]

Answer

[0,1][0,1]

Explanation

Solution

We have, 0≤cos−1(2x−1)≤π0 \le cos^{-1}\left(2x-1\right)\le\pi ⇒−1≤2x−1≤1\Rightarrow - 1 \le 2x - 1 \le 1 ⇒0≤2x≤2\Rightarrow 0 \le 2x \le 2 ⇒0≤x≤1\Rightarrow 0 \le x \le 1 ∴\therefore Domain of cos−1 (2x−1)=[0,1]cos^{-1}\,\left(2x - 1\right) = \left[0, 1\right]