What is the domain of f(x)=(x^2+5x)/(x^3-13x^2+36x) ?

The domain of f(x)=(x^2+5x)/(x^3-13x^2+36x) is x 9

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domain of f(x)=(x^2+5x)/(x^3-13x^2+36x)

domain

f (x) = \frac{x ^{2} + 5 x}{x ^{3} - 13 x ^{2} + 36 x}

x < 0 or 0 < x < 4 or 4 < x < 9 or x > 9

Interval Notation

(- \infty, 0) \cup (0, 4) \cup (4, 9) \cup (9, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = 4, x = 9

The function domain

x < 0 or 0 < x < 4 or 4 < x < 9 or x > 9

\frac{\frac{11}{x}}{x + 2}

f (x) = (x + 4) = 0

ln (- x^{2} + 5 x - 2)

lo g_{2} (x + 1) + 3

What is the domain of f(x)=(x^2+5x)/(x^3-13x^2+36x) ?
The domain of f(x)=(x^2+5x)/(x^3-13x^2+36x) is x<0\lor 0<x<4\lor 4<x<9\lor x>9