What is the domain of f(x)=sqrt((2x)/(4x-8)) ?

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

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

domain

f (x) = \frac{2 x}{4 x - 8}

x \leq 0 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq 0 or x > 2

f (x) = lo g_{10} (x + 8)

f (x) = 6 x + 3

f (x) = x + 1 + 2

lo g_{3} (x - 7)

lo g_{3} (x - 8)

What is the domain of f(x)=sqrt((2x)/(4x-8)) ?
The domain of f(x)=sqrt((2x)/(4x-8)) is x<= 0\lor x>2