What is the domain of f(x)=sqrt((x^2-25)/(x^2+4x+4)) ?

The domain of f(x)=sqrt((x^2-25)/(x^2+4x+4)) is x = 5

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domain of f(x)=sqrt((x^2-25)/(x^2+4x+4))

domain

f (x) = \frac{x ^{2} - 25}{x ^{2} + 4 x + 4}

x \leq - 5 or x \geq 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 5

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

x \leq - 5 or x \geq 5

f (x) = 4 - x

f (x) = \frac{1}{4 - x ^{2}}

f (x) = x^{\frac{3}{7}}

\frac{x - 3}{x - 7} + x + 8

f (x) = x - 1

What is the domain of f(x)=sqrt((x^2-25)/(x^2+4x+4)) ?
The domain of f(x)=sqrt((x^2-25)/(x^2+4x+4)) is x<=-5\lor x>= 5