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

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

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

domain

f (x) = \frac{\frac{x}{1 + x}}{1 + \frac{x}{1 + x}}

x < - 1 or - 1 < x < - \frac{1}{2} or x > - \frac{1}{2}

Interval Notation

(- \infty, - 1) \cup (- 1, - \frac{1}{2}) \cup (- \frac{1}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{1}{2}, x = - 1

The function domain

x < - 1 or - 1 < x < - \frac{1}{2} or x > - \frac{1}{2}

x^{2} - 2

f (x) = 3 + sin (\frac{2 π}{3} x)

f (x) = ln (2 - 5 x^{2})

f (x) = 5^{- x}

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

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