What is the domain of f(x)=sqrt((4-x^2)/(x+1)) ?

The domain of f(x)=sqrt((4-x^2)/(x+1)) is x<=-2\lor-1<x<= 2

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domain of f(x)=sqrt((4-x^2)/(x+1))

domain

f (x) = \frac{4 - x ^{2}}{x + 1}

x \leq - 2 or - 1 < x \leq 2

Interval Notation

(- \infty, - 2] \cup (- 1, 2]

Solution steps

Find non-negative values for radicals:

x \leq - 2 or - 1 < x \leq 2

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x \leq - 2 or - 1 < x \leq 2

f (x) = arctan (5 x)

f (x) = 3 x^{4} + 4 x^{3}

y = - 2 (x - 12.5) + 5

x^{2} - 10

f (x) = 3

What is the domain of f(x)=sqrt((4-x^2)/(x+1)) ?
The domain of f(x)=sqrt((4-x^2)/(x+1)) is x<=-2\lor-1<x<= 2