What is the domain of f(x)=x+2ln(1+1/x) ?

The domain of f(x)=x+2ln(1+1/x) is x 0

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domain of f(x)=x+2ln(1+1/x)

domain

f (x) = x + 2 ln (1 + \frac{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

3 - (x + 1)^{2}

y = f (y, x) x = - 1 x

y = lo g_{10} (a) (x)

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

\frac{1 - x}{2 x - 3}

What is the domain of f(x)=x+2ln(1+1/x) ?
The domain of f(x)=x+2ln(1+1/x) is x<-1\lor x>0