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

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

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

domain

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

x < - 1 or - 1 < x \leq - \frac{2}{3} or 0 \leq x < 1 or x > 1

Interval Notation

(- \infty, - 1) \cup (- 1, - \frac{2}{3}] \cup [0, 1) \cup (1, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{2}{3} or x \geq 0

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x \leq - \frac{2}{3} or 0 \leq x < 1 or x > 1

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

\frac{5 t}{2 t ^{2} + 7}

lo g_{2} (x - 1)

f (x) = (x + 2) 2

f (x) = y + 2

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