What is the domain of g(x)=(sqrt(x-1))/(x-9) ?

The domain of g(x)=(sqrt(x-1))/(x-9) is 1 9

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domain of g(x)=(sqrt(x-1))/(x-9)

domain

g (x) = \frac{x - 1}{x - 9}

1 \leq x < 9 or x > 9

Interval Notation

[1, 9) \cup (9, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 9

Combine real regions and undefined points for final function domain

1 \leq x < 9 or x > 9

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