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

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

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

domain

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

x < - 5 or x \geq 4

Interval Notation

(- \infty, - 5) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

x < - 5 or x \geq 4

Find undefined (singularity) points:

x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or x \geq 4

f (x) = \frac{2}{3} x - 12

\frac{x + 4}{- 4 x + 3}

f (x) = \frac{3 x + 4}{x ^{2} + 7 x + 12}

arccos (e^{3 x})

f (x) = - 3 (x - 1)^{2} + 2

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