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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 0, x = 3, x = - 2

The function domain

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

f (x) = \frac{14 x}{x ^{2} + 49}

\frac{x ^{2} - 2 x - 1}{x + 1}

(- 1, 3), (8, - 5)

- 8 x^{2} + 4 x - 2

\frac{x ^{2} - 9 x + 39}{x - 7}

What is the domain of f(x)= 1/x+1/(x-3)+1/(x+2) ?
The domain of f(x)= 1/x+1/(x-3)+1/(x+2) is x<-2\lor-2<x<0\lor 0<x<3\lor x>3