What is the domain of f(x)=(|x+5|-2)/(sqrt(x-3)) ?

The domain of f(x)=(|x+5|-2)/(sqrt(x-3)) is x>3

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domain of f(x)=(|x+5|-2)/(sqrt(x-3))

domain

f (x) = \frac{∣ x + 5 ∣ - 2}{x - 3}

x > 3

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x > 3

\frac{2 x - 2}{x ^{2} + x} + 1

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

f (x) = \frac{2 x + 9}{x ^{2}}

f (x) = x^{2} - 25

y = 3

What is the domain of f(x)=(|x+5|-2)/(sqrt(x-3)) ?
The domain of f(x)=(|x+5|-2)/(sqrt(x-3)) is x>3