What is the domain of f(x)=(x^3+3x^2)/(x^2-7x+12) ?

The domain of f(x)=(x^3+3x^2)/(x^2-7x+12) is x 4

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domain of f(x)=(x^3+3x^2)/(x^2-7x+12)

domain

f (x) = \frac{x ^{3} + 3 x ^{2}}{x ^{2} - 7 x + 12}

x < 3 or 3 < x < 4 or x > 4

Interval Notation

(- \infty, 3) \cup (3, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = 3

The function domain

x < 3 or 3 < x < 4 or x > 4

What is the domain of f(x)=(x^3+3x^2)/(x^2-7x+12) ?
The domain of f(x)=(x^3+3x^2)/(x^2-7x+12) is x<3\lor 3<x<4\lor x>4