What is the domain of f(x)=(x^2+3x-4)/(x(x^2-5)) ?

The domain of f(x)=(x^2+3x-4)/(x(x^2-5)) is x sqrt(5)

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domain of f(x)=(x^2+3x-4)/(x(x^2-5))

domain

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

x < - 5 or - 5 < x < 0 or 0 < x < 5 or x > 5

Interval Notation

(- \infty, - 5) \cup (- 5, 0) \cup (0, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 5, x = 5

The function domain

x < - 5 or - 5 < x < 0 or 0 < x < 5 or x > 5

3 x - y = 2

f (x) = - x + 5

f (x) = \frac{1 - 3 x ^{3}}{2 x ^{3} - 6 x + 2}

\frac{3}{x - 1}

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 2

What is the domain of f(x)=(x^2+3x-4)/(x(x^2-5)) ?
The domain of f(x)=(x^2+3x-4)/(x(x^2-5)) is x<-sqrt(5)\lor-sqrt(5)<x<0\lor 0<x<sqrt(5)\lor x>sqrt(5)