What is the domain of f(x)= 1/(|x-4|-4) ?

The domain of f(x)= 1/(|x-4|-4) is x 8

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domain of f(x)= 1/(|x-4|-4)

domain

f (x) = \frac{1}{∣ x - 4 ∣ - 4}

x < 0 or 0 < x < 8 or x > 8

Interval Notation

(- \infty, 0) \cup (0, 8) \cup (8, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = 8

The function domain

x < 0 or 0 < x < 8 or x > 8

f (x) = 16 - x^{2} - 4 - x

g (x) = \frac{1}{3 x}

y = - 3

x = 3 - 2^{6 y + 1}

X^{2} + 2 X - 8

What is the domain of f(x)= 1/(|x-4|-4) ?
The domain of f(x)= 1/(|x-4|-4) is x<0\lor 0<x<8\lor x>8