What is the domain of f(x)=(3x-5e^x)/(x^2(x+4)) ?

The domain of f(x)=(3x-5e^x)/(x^2(x+4)) is x 0

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domain of f(x)=(3x-5e^x)/(x^2(x+4))

domain

f (x) = \frac{3 x - 5 e ^{x}}{x ^{2} ( x + 4 )}

x < - 4 or - 4 < x < 0 or x > 0

Interval Notation

(- \infty, - 4) \cup (- 4, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 4

The function domain

x < - 4 or - 4 < x < 0 or x > 0

f (x) = lo g_{2} (x - 4)

arcsin (3 x)

x^{2} + x - 6

y = \frac{x ^{2} - 1}{x - 1}

f (x) = x^{3} - 3 x + 5

What is the domain of f(x)=(3x-5e^x)/(x^2(x+4)) ?
The domain of f(x)=(3x-5e^x)/(x^2(x+4)) is x<-4\lor-4<x<0\lor x>0