What is the domain of f(x)=(x^2-9)/(x^2-2x-1) ?

The domain of f(x)=(x^2-9)/(x^2-2x-1) is x 1+sqrt(2)

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domain of f(x)=(x^2-9)/(x^2-2x-1)

domain

x < 1 - 2 or 1 - 2 < x < 1 + 2 or x > 1 + 2

Interval Notation

(- \infty, 1 - 2) \cup (1 - 2, 1 + 2) \cup (1 + 2, \infty)

Solution steps

Find undefined (singularity) points:

x = 1 + 2, x = 1 - 2

The function domain

x < 1 - 2 or 1 - 2 < x < 1 + 2 or x > 1 + 2

What is the domain of f(x)=(x^2-9)/(x^2-2x-1) ?
The domain of f(x)=(x^2-9)/(x^2-2x-1) is x<1-sqrt(2)\lor 1-sqrt(2)<x<1+sqrt(2)\lor x>1+sqrt(2)