What is the domain of f(x)=(ln(x+5))/(x^2-2x-3) ?

The domain of f(x)=(ln(x+5))/(x^2-2x-3) is -5 3

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domain of f(x)=(ln(x+5))/(x^2-2x-3)

domain

f (x) = \frac{ln ( x + 5 )}{x ^{2} - 2 x - 3}

- 5 < x < - 1 or - 1 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find positive values for logs:

x > - 5

Find undefined (singularity) points:

x = 3, x = - 1

Combine real regions and undefined points for final function domain

- 5 < x < - 1 or - 1 < x < 3 or x > 3

h (x) = x^{2} + 16

f (x) = (\frac{2}{3})^{x - 3} - 2

R (x, y) = y x^{2} - 4 y - x^{2} = 0

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

\frac{8 x + 5}{2 - 5 x}

What is the domain of f(x)=(ln(x+5))/(x^2-2x-3) ?
The domain of f(x)=(ln(x+5))/(x^2-2x-3) is -5<x<-1\lor-1<x<3\lor x>3