What is the domain of f(x)=(x+3)/(3x-27)+1/(x^2-4) ?

The domain of f(x)=(x+3)/(3x-27)+1/(x^2-4) is x 9

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domain of f(x)=(x+3)/(3x-27)+1/(x^2-4)

domain

f (x) = \frac{x + 3}{3 x - 27} + \frac{1}{x ^{2} - 4}

x < - 2 or - 2 < x < 2 or 2 < x < 9 or x > 9

Interval Notation

(- \infty, - 2) \cup (- 2, 2) \cup (2, 9) \cup (9, \infty)

Solution steps

Find undefined (singularity) points:

x = 9, x = 2, x = - 2

The function domain

x < - 2 or - 2 < x < 2 or 2 < x < 9 or x > 9

d o main \frac{10 - x}{x ^{2} - 1}

p a r a ll e l y = - 3 + 5

d o main y = cos (x)

a sy m pt o t es f (x) = \frac{6 x ^{2} - 1}{x ^{2} - 6 x + 9}

m = - 6, at (3 - 1)

What is the domain of f(x)=(x+3)/(3x-27)+1/(x^2-4) ?
The domain of f(x)=(x+3)/(3x-27)+1/(x^2-4) is x<-2\lor-2<x<2\lor 2<x<9\lor x>9