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

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

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

domain

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

x < - 2 or - 2 < x < 0 or x > 0

Interval Notation

(- \infty, - 2) \cup (- 2, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = - 2, x = 0

The function domain

x < - 2 or - 2 < x < 0 or x > 0

3 x + 2

f (x) = - 2 - x

f (x) = ∣ x + 6 ∣

f (x) = \frac{5}{x + 5}

x - 2 + 1

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