What is the domain of f(x)=(2x-7)/(sqrt(x^2-5x+6)) ?

The domain of f(x)=(2x-7)/(sqrt(x^2-5x+6)) is x 3

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domain of f(x)=(2x-7)/(sqrt(x^2-5x+6))

domain

f (x) = \frac{2 x - 7}{x ^{2} - 5 x + 6}

x < 2 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 2 or x \geq 3

Find undefined (singularity) points:

x = 3, x = 2

Combine real regions and undefined points for final function domain

x < 2 or x > 3

d o main f (x) = - \frac{x}{( 1 - x ^{2} ) ( 5 - x )}

d o main f (x) = \frac{x}{2 x + 1}

in t erce pt s f (x) = - 5 x + 1

in v erse \frac{x - 4}{5}

in t erce pt s f (x) = 5

What is the domain of f(x)=(2x-7)/(sqrt(x^2-5x+6)) ?
The domain of f(x)=(2x-7)/(sqrt(x^2-5x+6)) is x<2\lor x>3