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

f (x) = ln (1 + \frac{x + 1}{x + 4})

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}

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

f (x) = - 2 x

cos (4 x)

f (x) = 3 cos (x)

\frac{1}{4} x^{4} - 2 x^{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