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

The domain of f(x)=(sqrt(2-x))/(ln(x)) is 0<x<1\lor 1<x<= 2

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

domain

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

0 < x < 1 or 1 < x \leq 2

Interval Notation

(0, 1) \cup (1, 2]

Solution steps

Find non-negative values for radicals:

x \leq 2

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

0 < x < 1 or 1 < x \leq 2

f (x) = \frac{x - 6}{x ^{2} - 3 x - 18}

e^{2 x + 3}

f (x) = 2 x^{2} - 11 x + 12 + 1

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

\frac{x - 5}{x ^{2} - 4 x}

What is the domain of f(x)=(sqrt(2-x))/(ln(x)) ?
The domain of f(x)=(sqrt(2-x))/(ln(x)) is 0<x<1\lor 1<x<= 2