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

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

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

domain

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

x < - 2 - 3 or - 2 - 3 < x < - 2 + 3 or x > - 2 + 3

Interval Notation

(- \infty, - 2 - 3) \cup (- 2 - 3, - 2 + 3) \cup (- 2 + 3, \infty)

Solution steps

Find undefined (singularity) points:

x = - 2 + 3, x = - 2 - 3

The function domain

x < - 2 - 3 or - 2 - 3 < x < - 2 + 3 or x > - 2 + 3

\frac{x + 4}{x ( x + 12 )}

f (x) = lo g_{\frac{1}{7}} (x)

g (x) = \frac{3 x + 1}{x + 8}

f (x) = \frac{5 x - 15}{x ^{2} - 9}

f (x) = \frac{1}{x - 5 - 2} + ln (x + 5)

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