The value of y for which the expression `p = 1/((|y - 1| -3))` becomes undefined:

Options

A. `{2,8}`
B. `{-2, 4}`
C. `{-1, 3}`
D. `{1,2}`

Answer

To determine the value of \( y \) for which the expression \( p = \frac{1}{|y - 1| - 3} \) becomes undefined, we need to find when the denominator equals zero.

### Step-by-step Solution:

1. **Set the Denominator to Zero**:
We start by setting the denominator of the expression equal to zero:
\[ |y - 1| - 3 = 0 \]

2. **Solve for the Absolute Value**:
Rearranging the equation gives:
\[ |y - 1| = 3 \]

3. **Consider the Cases for Absolute Value**:
The absolute value equation \( |y - 1| = 3 \) can be split into two cases:
- Case 1: \( y - 1 = 3 \)
- Case 2: \( y - 1 = -3 \)

4. **Solve Each Case**:
- For Case 1:
\[ y - 1 = 3 \implies y = 3 + 1 = 4 \]
- For Case 2:
\[ y - 1 = -3 \implies y = -3 + 1 = -2 \]

5. **Conclusion**:
The values of \( y \) for which the expression becomes undefined are \( y = 4 \) and \( y = -2 \).

### Final Answer:
The expression \( p \) becomes undefined for \( y = 4 \) and \( y = -2 \).

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