What is the domain of f(x)=(1+x-3x^2)/(xsqrt(x^2-4)) ?

The domain of f(x)=(1+x-3x^2)/(xsqrt(x^2-4)) is x 2

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domain of f(x)=(1+x-3x^2)/(xsqrt(x^2-4))

domain

f (x) = \frac{1 + x - 3 x ^{2}}{x x ^{2} - 4}

x < - 2 or x > 2

Interval Notation

(- \infty, - 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 2

(x - 3)^{2} + 4

f (x) = x e^{2 x}

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

\frac{1 + x ^{2}}{4 - x ^{2}}

What is the domain of f(x)=(1+x-3x^2)/(xsqrt(x^2-4)) ?
The domain of f(x)=(1+x-3x^2)/(xsqrt(x^2-4)) is x<-2\lor x>2