What is the domain of ln(8/(x+4)+4) ?

The domain of ln(8/(x+4)+4) is x -4

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domain of ln(8/(x+4)+4)

domain

ln (\frac{8}{x + 4} + 4)

x < - 6 or x > - 4

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 6 or x > - 4

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

x < - 6 or x > - 4

f (x) = 3 + 6 x - 8 x^{2}

f (x) = 2 x + 1 - 4

(5 x - 6) (2 x^{2})

f (x) = \frac{3 x ^{2} + 6 x + 9}{x ^{2} + 4 x + 3}

f (x) = \frac{( 11 )}{x - 4}

What is the domain of ln(8/(x+4)+4) ?
The domain of ln(8/(x+4)+4) is x<-6\lor x>-4