What is the domain of f(x)=ln(1+((x+1))/(x+4)) ?

The domain of f(x)=ln(1+((x+1))/(x+4)) is x -5/2

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domain of f(x)=ln(1+((x+1))/(x+4))

domain

x < - 4 or x > - \frac{5}{2}

Interval Notation

(- \infty, - 4) \cup (- \frac{5}{2}, \infty)

Solution steps

Find positive values for logs:

x < - 4 or x > - \frac{5}{2}

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or x > - \frac{5}{2}

What is the domain of f(x)=ln(1+((x+1))/(x+4)) ?
The domain of f(x)=ln(1+((x+1))/(x+4)) is x<-4\lor x>-5/2