What is the domain of f(x)=(x^3-4x^2+3x)/(x^2-5x+4) ?

The domain of f(x)=(x^3-4x^2+3x)/(x^2-5x+4) is x 4

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domain of f(x)=(x^3-4x^2+3x)/(x^2-5x+4)

domain

f (x) = \frac{x ^{3} - 4 x ^{2} + 3 x}{x ^{2} - 5 x + 4}

x < 1 or 1 < x < 4 or x > 4

Interval Notation

(- \infty, 1) \cup (1, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = 1

The function domain

x < 1 or 1 < x < 4 or x > 4

f (x) = \frac{x ^{2} + 3 x - 4}{x ^{2} - x - 6}

- 16 x^{2} - 49 x

- 6 x^{2} (5 x - 3)

f (x) = \frac{x ^{2}}{x ^{2} + x - 20}

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

What is the domain of f(x)=(x^3-4x^2+3x)/(x^2-5x+4) ?
The domain of f(x)=(x^3-4x^2+3x)/(x^2-5x+4) is x<1\lor 1<x<4\lor x>4