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

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

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

domain

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

x < 2 or 2 < x < 3

Interval Notation

(- \infty, 2) \cup (2, 3)

Solution steps

Find positive values for logs:

x < 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or 2 < x < 3

f (x) = 2 x, - 1 \leq x \leq 5

\frac{2}{x + 2}

(x^{3}) (4 x^{2} + 17 x - 15)

f (x) = \frac{x - 1}{x 1 - x} - \frac{x + 1}{13}

f (x) = 3 x - 9, - 1 \leq x \leq 7

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