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 x>= 3

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

domain

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

x \geq 3

Interval Notation

[3, \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

x \geq 3

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

200 - 4 x

f (x) = \frac{( x 5 ^{x} )}{5 ^{(x + 2)} - 6}

\frac{x}{ln ( x - 1 ) - 1}

f (x) = \frac{x + 1}{x ^{2} - 9 x + 8}

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 x>= 3