What is the domain of f(x)=(ln(x))/(x^2-5x+6) ?

The domain of f(x)=(ln(x))/(x^2-5x+6) is 0 3

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domain of f(x)=(ln(x))/(x^2-5x+6)

domain

f (x) = \frac{ln ( x )}{x ^{2} - 5 x + 6}

0 < x < 2 or 2 < x < 3 or x > 3

Interval Notation

(0, 2) \cup (2, 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 3, x = 2

Combine real regions and undefined points for final function domain

0 < x < 2 or 2 < x < 3 or x > 3

\frac{x ^{2} - 4}{3 x - 1}

\frac{8 x}{7 x - 4}

f (x) = 2 x^{3} + 11 x^{2} - 8 x - 12

11 x - 9

9 - 5 x^{2}

What is the domain of f(x)=(ln(x))/(x^2-5x+6) ?
The domain of f(x)=(ln(x))/(x^2-5x+6) is 0<x<2\lor 2<x<3\lor x>3