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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

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

2^{- x} + 4

x + 4

(1.3, 7.8), (6.5, 1.1)

(2.7) (- 6.3)

f (x) = x^{2} - 6 x + 5

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