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

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

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

domain

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

1 \leq x < 2 or 2 < x < 3

Interval Notation

Solution steps

Find non-negative values for radicals:

x \geq 1

Find positive values for logs:

x < 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 \leq x < 2 or 2 < x < 3

- \frac{1}{x ^{2} 1 - x ^{2}}

x + 8

f (x) = lo g_{10} (5) (4 - x)

\frac{2 x ^{2} - 14 x + 24}{x ^{2} + 6 x - 40}

y = - x - 1 + 4

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