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

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

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

domain

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

x < 4 or 4 < x \leq 8

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 8

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < 4 or 4 < x \leq 8

f (x) = \frac{2 x}{3 x + 1}

f (x) = ∣ x + 5 ∣

f (x) = \frac{x + 5}{x ^{2} - x - 6}

f (x) = 2.5 x + 3.5

f (x) = x - 2 - 1

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