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 < 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 = 5, x = - 1, x = 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 1 or 1 < x < 5

- 16 x^{2} + 20

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

x^{2} - 20 x + 100

x^{3} + 8 x^{2} - 9 x - 72

f (x) = - 5 x + 1

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