What is the domain of y=(x^2-25)/(log_{5)(x^2+4x+4)} ?

The domain of y=(x^2-25)/(log_{5)(x^2+4x+4)} is x -1

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domain of y=(x^2-25)/(log_{5)(x^2+4x+4)}

domain

y = \frac{x ^{2} - 25}{lo g _{5} ( x ^{2} + 4 x + 4 )}

x < - 3 or - 3 < x < - 2 or - 2 < x < - 1 or x > - 1

Interval Notation

(- \infty, - 3) \cup (- 3, - 2) \cup (- 2, - 1) \cup (- 1, \infty)

Solution steps

Find positive values for logs:

x < - 2 or x > - 2

Find undefined (singularity) points:

x = - 1, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x < - 2 or - 2 < x < - 1 or x > - 1

f (x) = \frac{( x - 6 )}{x ^{2} - 1}

f (x) = \frac{x ^{2} - 6}{x ^{2} - 1}

g (x) = 4 lo g_{10} (x) + 4

f (x) = \frac{x + 5}{x ^{\frac{3}{2}}}

f (x) = 3 csc (3 x + π) - 2

What is the domain of y=(x^2-25)/(log_{5)(x^2+4x+4)} ?
The domain of y=(x^2-25)/(log_{5)(x^2+4x+4)} is x<-3\lor-3<x<-2\lor-2<x<-1\lor x>-1