The equation of image of pair of lines `y=|x-1|` with respect to y-axis is :

Options

A. y=|x+1|
B. y=|x-1|+3
C. `x^2-y^2+2x+1=0`
D. `x^2-y^2+2x-1=0`

Answer

To solve the problem of finding the equation of the image of the pair of lines given by \( y = |x - 1| \) with respect to the y-axis, we can follow these steps:

### Step 1: Understand the given equation
The equation \( y = |x - 1| \) represents two lines:
1. For \( x - 1 \geq 0 \) (or \( x \geq 1 \)), \( y = x - 1 \).
2. For \( x - 1 < 0 \) (or \( x < 1 \)), \( y = -(x - 1) = -x + 1 \).