What is the domain of f(x)=(sqrt(5-x))/(-4x+8) ?

The domain of f(x)=(sqrt(5-x))/(-4x+8) is x<2\lor 2<x<= 5

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domain of f(x)=(sqrt(5-x))/(-4x+8)

domain

f (x) = \frac{5 - x}{- 4 x + 8}

x < 2 or 2 < x \leq 5

Interval Notation

(- \infty, 2) \cup (2, 5]

Solution steps

Find non-negative values for radicals:

x \leq 5

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or 2 < x \leq 5

What is the domain of f(x)=(sqrt(5-x))/(-4x+8) ?
The domain of f(x)=(sqrt(5-x))/(-4x+8) is x<2\lor 2<x<= 5