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

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

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domain of g(x)=(sqrt(x-1))/(x-3)

domain

g (x) = \frac{x - 1}{x - 3}

1 \leq x < 3 or x > 3

Interval Notation

[1, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

1 \leq x < 3 or x > 3

\frac{2 x}{x + 1}

f (x) = t - 5

f (x) = \frac{2 x + 5}{x ^{2} + 2 x - 48}

f (x) = \frac{∣ x - 2 ∣}{x - 2}

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