What is the domain of f(x)=ln((2x+7)/(x^2-x-20)) ?

The domain of f(x)=ln((2x+7)/(x^2-x-20)) is -4 5

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domain of f(x)=ln((2x+7)/(x^2-x-20))

domain

f (x) = ln (\frac{2 x + 7}{x ^{2} - x - 20})

- 4 < x < - \frac{7}{2} or x > 5

Interval Notation

(- 4, - \frac{7}{2}) \cup (5, \infty)

Solution steps

Find positive values for logs:

- 4 < x < - \frac{7}{2} or x > 5

Find undefined (singularity) points:

x = 5, x = - 4

Combine real regions and undefined points for final function domain

- 4 < x < - \frac{7}{2} or x > 5

f (x) = 9 x^{3} + 5

(\frac{2}{3})^{x}

f (x) = 2 x^{3} - 3 x^{2} - 36 x

f (x) = 4 x^{2} - 8

f (x) = y + e^{y}

What is the domain of f(x)=ln((2x+7)/(x^2-x-20)) ?
The domain of f(x)=ln((2x+7)/(x^2-x-20)) is -4<x<-7/2 \lor x>5