The domain of definition of `cos^(-1)(2x-1)` is

Options

A. `[-1,1]`
B. `[0,1]`
C. `[-1,0]`
D. `[0,2]`

Explanation

To find the domain of the function \( \cos^{-1}(2x - 1) \), we need to ensure that the expression inside the inverse cosine function lies within the valid range for the cosine inverse function. The range of \( \cos^{-1}(y) \) is defined for \( y \) values in the interval \([-1, 1]\).

### Step-by-Step Solution:

1. **Set up the inequality**:
We need to find the values of \( x \) for which:
\[ -1 \leq 2x - 1 \leq 1 \]

2. **Solve the left part of the inequality**:
\[ -1 \leq 2x - 1 \]
Add 1 to both sides:
\[ 0 \leq 2x \]
Divide both sides by 2:
\[ 0 \leq x \]
This simplifies to:
\[ x \geq 0 \]

3. **Solve the right part of the inequality**:
\[ 2x - 1 \leq 1 \]
Add 1 to both sides:
\[ 2x \leq 2 \]
Divide both sides by 2:
\[ x \leq 1 \]

4. **Combine the results**:
From the two inequalities, we have:
\[ 0 \leq x \leq 1 \]
This means that the domain of \( \cos^{-1}(2x - 1) \) is:
\[ [0, 1] \]

### Final Answer:
The domain of definition of \( \cos^{-1}(2x - 1) \) is \( [0, 1] \).