What is the domain of f(x)=(sqrt(x^2-36))/(2x-8) ?

The domain of f(x)=(sqrt(x^2-36))/(2x-8) is x = 6

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domain of f(x)=(sqrt(x^2-36))/(2x-8)

domain

x \leq - 6 or x \geq 6

Interval Notation

(- \infty, - 6] \cup [6, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 6 or x \geq 6

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq - 6 or x \geq 6

What is the domain of f(x)=(sqrt(x^2-36))/(2x-8) ?
The domain of f(x)=(sqrt(x^2-36))/(2x-8) is x<=-6\lor x>= 6