What is the domain of f(x)=(sqrt(4-x))/(ln(x-2)) ?

The domain of f(x)=(sqrt(4-x))/(ln(x-2)) is 2<x<3\lor 3<x<= 4

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domain of f(x)=(sqrt(4-x))/(ln(x-2))

domain

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

2 < x < 3 or 3 < x \leq 4

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 4

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 < x < 3 or 3 < x \leq 4

2^{2 + x}

y = 49 - x^{2}

\frac{5 x}{2 x ^{2} + 7}

1^{s i n (x)}

y = \frac{2 x ^{3}}{x ^{2} + 1}

What is the domain of f(x)=(sqrt(4-x))/(ln(x-2)) ?
The domain of f(x)=(sqrt(4-x))/(ln(x-2)) is 2<x<3\lor 3<x<= 4