What is the domain of f(x)= 1/(log_{10)(x^2+10x+25)} ?

The domain of f(x)= 1/(log_{10)(x^2+10x+25)} is x -4

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domain of f(x)= 1/(log_{10)(x^2+10x+25)}

domain

f (x) = \frac{1}{lo g _{10} ( x ^{2} + 10 x + 25 )}

x < - 6 or - 6 < x < - 5 or - 5 < x < - 4 or x > - 4

Interval Notation

(- \infty, - 6) \cup (- 6, - 5) \cup (- 5, - 4) \cup (- 4, \infty)

Solution steps

Find positive values for logs:

x < - 5 or x > - 5

Find undefined (singularity) points:

x = - 4, x = - 6

Combine real regions and undefined points for final function domain

x < - 6 or - 6 < x < - 5 or - 5 < x < - 4 or x > - 4

f (x) = \frac{( x + 3 )}{( x - 4 )}

f (x) = - - x + 3

f (x) = 4 x^{3} - 24 x^{2} + 200 x

f (x) = 3 x - 6

f (x) = - - x + 2

What is the domain of f(x)= 1/(log_{10)(x^2+10x+25)} ?
The domain of f(x)= 1/(log_{10)(x^2+10x+25)} is x<-6\lor-6<x<-5\lor-5<x<-4\lor x>-4