For the function \( f(x)=|2 x-1|-3 \), find the values of \( x \) such that \( f(x)=0 \) List your answers separated by a comma. For example, if you found the solutions \( x=1 \) and \( x=2 \), you would enter 1,2 .

To find the values of \( x \) such that \( f(x) = 0 \) for the function \( f(x)=|2 x-1|-3 \), we set up the equation: \[ |2x - 1| - 3 = 0 \] Adding 3 to both sides gives: \[ |2x - 1| = 3 \] This absolute value equation can be split into two cases: 1. \( 2x - 1 = 3 \) 2. \( 2x - 1 = -3 \) Solving the first case: \[ 2x - 1 = 3 \implies 2x = 4 \implies x = 2 \] Solving the second case: \[ 2x - 1 = -3 \implies 2x = -2 \implies x = -1 \] Thus, the values of \( x \) that satisfy \( f(x) = 0 \) are: \[ -1, 2 \]