What is the domain of f(x)=(sqrt(x-4))/(2x-16) ?

The domain of f(x)=(sqrt(x-4))/(2x-16) is 4 8

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domain of f(x)=(sqrt(x-4))/(2x-16)

domain

f (x) = \frac{x - 4}{2 x - 16}

4 \leq x < 8 or x > 8

Interval Notation

[4, 8) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 4

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

4 \leq x < 8 or x > 8

What is the domain of f(x)=(sqrt(x-4))/(2x-16) ?
The domain of f(x)=(sqrt(x-4))/(2x-16) is 4<= x<8\lor x>8