What is the domain of f(x)= x/(1-x^2)+sqrt(5-x) ?

The domain of f(x)= x/(1-x^2)+sqrt(5-x) is x<-1\lor-1<x<1\lor 1<x<= 5

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domain of f(x)= x/(1-x^2)+sqrt(5-x)

domain

f (x) = \frac{x}{1 - x ^{2}} + 5 - x

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 5

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

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

\frac{3 x + 6}{x ^{2} - x - 2}

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

\frac{- 10 x ^{2} + 13 x + 3}{3 x ^{2} + 7 x - 6}

\frac{x + 4}{x ^{2} - 9}

What is the domain of f(x)= x/(1-x^2)+sqrt(5-x) ?
The domain of f(x)= x/(1-x^2)+sqrt(5-x) is x<-1\lor-1<x<1\lor 1<x<= 5