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

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

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

domain

f (x) = \frac{x}{x - 1 - 1}

1 \leq x < 2 or x > 2

Interval Notation

[1, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 \leq x < 2 or x > 2

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