What is the domain of f(x)= 1/(x^2-5x+6) ?

The domain of f(x)= 1/(x^2-5x+6) is x 3

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domain of f(x)= 1/(x^2-5x+6)

domain

f (x) = \frac{1}{x ^{2} - 5 x + 6}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 3, x = 2

The function domain

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

y = - 2 x + 2

f (x) = \frac{3 x ^{2} + 5 x - 7}{x ^{2} - 3}

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

f (x) = 5 x - 12 = 0

\frac{x}{x ^{2} + 49}

What is the domain of f(x)= 1/(x^2-5x+6) ?
The domain of f(x)= 1/(x^2-5x+6) is x<2\lor 2<x<3\lor x>3