Find Where Undefined/Discontinuous f(x)=(x-2)/(|x-1|)

$f (x) = \frac{x - 2}{| x - 1 |}$

Step 1

Set the denominator in $\frac{x - 2}{| x - 1 |}$ equal to $0$ to find where the expression is undefined.

$| x - 1 | = 0$

Step 2

Solve for $x$ .

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 1 = \pm 0$

Plus or minus $0$ is $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 3