Find Where Undefined/Discontinuous (x^2-4)/(x-2)

Problem

(x2−4)/(x−2)

Solution

1. Identify the type of function. This is a rational function, which is undefined and discontinuous at any x value that makes the denominator equal to zero.

2. Set the denominator equal to zero to find the points of discontinuity.

x−2=0

3. Solve for x by adding 2 to both sides of the equation.

x=2

4. Determine the nature of the discontinuity. Since the numerator x2−4 also equals zero at x=2 this is a removable discontinuity (a hole), but the function remains undefined at that point.

Final Answer

Undefined/Discontinuous at *x=2

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