Determine the domain of the function.

y =

**Solution:-**

The numerator can be any number. Values of x for which the expression is undefined are values that make the denominator equal to 0.

Set the denominator equal to zero to find these values.

x^{2} + 2x -8 = 0

Factor the denominator.

(x + 4 )(x-2) = 0

Solve the equation to obtain the values of x that are exchange in the given expression.

x + 4 = 0 or x- 2 = 0

x = -4 or x = 2

The domain of the original function is {x | x ≠ – 4 and x ≠ 2}