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

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

domain

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

x < - 9 or x > 0

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 9 or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < - 9 or x > 0

f (x) = sin (x)

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

y = \frac{x - 4}{x ^{2} - 2 x - 3}

y = ln (x + 3)

f (x) = - (\frac{1}{2})^{x}

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\lor x>0