What is the domain of f(x)=(3/(x-2))/(sqrt(x-1)) ?

The domain of f(x)=(3/(x-2))/(sqrt(x-1)) is 1 2

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domain of f(x)=(3/(x-2))/(sqrt(x-1))

domain

f (x) = \frac{\frac{3}{x - 2}}{x - 1}

1 < 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 = 1, x = 2

Combine real regions and undefined points for final function domain

1 < x < 2 or x > 2

What is the domain of f(x)=(3/(x-2))/(sqrt(x-1)) ?
The domain of f(x)=(3/(x-2))/(sqrt(x-1)) is 1<x<2\lor x>2