What is the domain of f(x)=log_{5}(((x+1))/x) ?

The domain of f(x)=log_{5}(((x+1))/x) is x 0

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domain of f(x)=log_{5}(((x+1))/x)

domain

f (x) = lo g_{5} (\frac{( x + 1 )}{x})

x < - 1 or x > 0

Interval Notation

(- \infty, - 1) \cup (0, \infty)

Solution steps

Find positive values for logs:

x < - 1 or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < - 1 or x > 0

What is the domain of f(x)=log_{5}(((x+1))/x) ?
The domain of f(x)=log_{5}(((x+1))/x) is x<-1\lor x>0