What is the domain of 1/(x^2)+1/(x+1)+sqrt(1-x) ?

The domain of 1/(x^2)+1/(x+1)+sqrt(1-x) is x<-1\lor-1<x<0\lor 0<x<= 1

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domain of 1/(x^2)+1/(x+1)+sqrt(1-x)

domain

\frac{1}{x ^{2}} + \frac{1}{x + 1} + 1 - x

x < - 1 or - 1 < x < 0 or 0 < x \leq 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = 0, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 0 or 0 < x \leq 1

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