What is the domain of f(x)=(sqrt(x-3))/(ln(x-1)) ?

The domain of f(x)=(sqrt(x-3))/(ln(x-1)) is x>= 3

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domain of f(x)=(sqrt(x-3))/(ln(x-1))

domain

x \geq 3

Interval Notation

[3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 3

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \geq 3

What is the domain of f(x)=(sqrt(x-3))/(ln(x-1)) ?
The domain of f(x)=(sqrt(x-3))/(ln(x-1)) is x>= 3