What is the domain of f(x)=(sqrt(x^2-5x+6))/(x+4) ?

The domain of f(x)=(sqrt(x^2-5x+6))/(x+4) is x = 3

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domain of f(x)=(sqrt(x^2-5x+6))/(x+4)

domain

f (x) = \frac{x ^{2} - 5 x + 6}{x + 4}

x < - 4 or - 4 < x \leq 2 or x \geq 3

Interval Notation

(- \infty, - 4) \cup (- 4, 2] \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 2 or x \geq 3

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or - 4 < x \leq 2 or x \geq 3

ln ∣ x - 3 ∣ \cdot (x - 1) (5 - x)

f (x) = 2 x^{2} - 8

f (x) = 2 e^{x - 2} + 3

f (x) = 2 x^{2} - 12 x + 13

f (x) = ln (x - 4) + x

What is the domain of f(x)=(sqrt(x^2-5x+6))/(x+4) ?
The domain of f(x)=(sqrt(x^2-5x+6))/(x+4) is x<-4\lor-4<x<= 2\lor x>= 3