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 1 2

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

domain

f (x) = \frac{x + 3}{ln ( 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 - 3

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 < x < 2 or x > 2

\frac{4}{x + 1}

f (x) = - x^{2} + 2 x + 1

2 x^{2} - 7 x - 6

f (x) = ln (64 - x^{2})

f (x) = \frac{x + 3}{2 x - 4}

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 1<x<2\lor x>2