What is the domain of f(x)=(sqrt(2x^2)-x-1)/(x^2+3x) ?

The domain of f(x)=(sqrt(2x^2)-x-1)/(x^2+3x) is x 0

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domain of f(x)=(sqrt(2x^2)-x-1)/(x^2+3x)

domain

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

x < - 3 or - 3 < x < 0 or x > 0

Interval Notation

(- \infty, - 3) \cup (- 3, 0) \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

Find undefined (singularity) points:

x = 0, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x < 0 or x > 0

\frac{x + 5}{x ^{2} + 3 x - 10}

- 1 + 2 - x

f (x) = x - 11 + 5

- 2 + \frac{1}{x}

\frac{x}{( x + 2 ) ^{2}}

What is the domain of f(x)=(sqrt(2x^2)-x-1)/(x^2+3x) ?
The domain of f(x)=(sqrt(2x^2)-x-1)/(x^2+3x) is x<-3\lor-3<x<0\lor x>0