What is the domain of f(x)=(sqrt(5-x))/(x+1) ?

The domain of f(x)=(sqrt(5-x))/(x+1) is x<-1\lor-1<x<= 5

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domain of f(x)=(sqrt(5-x))/(x+1)

domain

f (x) = \frac{5 - x}{x + 1}

x < - 1 or - 1 < x \leq 5

Interval Notation

(- \infty, - 1) \cup (- 1, 5]

Solution steps

Find non-negative values for radicals:

x \leq 5

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x \leq 5

\frac{3 x - 2}{x ^{3} - 9 x}

∣ x ∣ + ∣ x - 1 ∣

f (x) = x^{3} + 2 x

ln (4 x - x^{2})

f (x) = 3 x^{2} - 4 x - 5

What is the domain of f(x)=(sqrt(5-x))/(x+1) ?
The domain of f(x)=(sqrt(5-x))/(x+1) is x<-1\lor-1<x<= 5