What is the domain of f(x)=log_{2}((x-9)/x) ?

The domain of f(x)=log_{2}((x-9)/x) is x 9

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domain of f(x)=log_{2}((x-9)/x)

domain

f (x) = lo g_{2} (\frac{x - 9}{x})

x < 0 or x > 9

Interval Notation

(- \infty, 0) \cup (9, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 9

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or x > 9

What is the domain of f(x)=log_{2}((x-9)/x) ?
The domain of f(x)=log_{2}((x-9)/x) is x<0\lor x>9