What is the domain of y=ln(((x+1)*(x+2))/(x+3)) ?

The domain of y=ln(((x+1)*(x+2))/(x+3)) is -3 -1

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domain of y=ln(((x+1)*(x+2))/(x+3))

domain

y = ln (\frac{( x + 1 ) \cdot ( x + 2 )}{x + 3})

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

Interval Notation

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

Solution steps

Find positive values for logs:

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

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

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

f (x) = x^{3} - 4 x^{2} - 19 x - 14

y = - 16 x^{2} + 275 x + 127

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

f (x) = (x - 3)^{2} - 5

y = lo g_{10} (x) - 2

What is the domain of y=ln(((x+1)*(x+2))/(x+3)) ?
The domain of y=ln(((x+1)*(x+2))/(x+3)) is -3<x<-2\lor x>-1