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

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

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

domain

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

1 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - \frac{3}{2}

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

1 < x < 3 or x > 3

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