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 for \( \cos^{-1}(x) \) is defined for \( x \) values between -1 and 1, inclusive.

### Step-by-Step Solution:

1. **Set Up the Inequality**:
Since \( \cos^{-1}(x) \) is defined for \( -1 \leq x \leq 1 \), we set up the inequality for our function:
\[ -1 \leq 2x - 1 \leq 1 \]

2. **Break Down the Inequality**:
We can break this compound inequality into two separate inequalities:
\[ 2x - 1 \geq -1 \quad \text{and} \quad 2x - 1 \leq 1 \]

3. **Solve the First Inequality**:
For the first inequality \( 2x - 1 \geq -1 \):
\[ 2x \geq 0 \quad \Rightarrow \quad x \geq 0 \]

4. **Solve the Second Inequality**:
For the second inequality \( 2x - 1 \leq 1 \):
\[ 2x \leq 2 \quad \Rightarrow \quad x \leq 1 \]

5. **Combine the Results**:
From the two inequalities, we find that:
\[ 0 \leq x \leq 1 \]
This can be written in interval notation as:
\[ [0, 1] \]

6. **Conclusion**:
Therefore, the domain of the function \( \cos^{-1}(2x - 1) \) is:
\[ [0, 1] \]

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