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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 0, x = 4

The function domain

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

f (x) = 3^{x - 1}

8 x + 5

f (x) = 8 x + 40

f (x) = x^{2} - 4 x + 2

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\lor 0<x<4\lor x>4