What is the domain of f(x)=log_{3}(x/(x-3)+2) ?

The domain of f(x)=log_{3}(x/(x-3)+2) is x 3

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domain of f(x)=log_{3}(x/(x-3)+2)

domain

f (x) = lo g_{3} (\frac{x}{x - 3} + 2)

x < 2 or x > 3

Interval Notation

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

Solution steps

Find positive values for logs:

x < 2 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 2 or x > 3

f (x) = e^{3} x

f (x) = ln (ln (ln (x)))

y = x 8 - x^{2}

f (x) = \frac{4 - 3 x}{2 x - 11}

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