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

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

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

domain

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

x < 2 or 2 < x \leq 5

Interval Notation

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

f (x) = \frac{9}{8 x + 9}

g (x) = \frac{x}{x ^{2} + 36}

f (x) = 2 x^{2} - 2 x + 1

\frac{900}{56}

\frac{1}{4 - 2 x}

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