What is the domain of f(x)=ln(1/((x^2-3x-28))) ?

The domain of f(x)=ln(1/((x^2-3x-28))) is x 7

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domain of f(x)=ln(1/((x^2-3x-28)))

domain

f (x) = ln (\frac{1}{( x ^{2} - 3 x - 28 )})

x < - 4 or x > 7

Interval Notation

(- \infty, - 4) \cup (7, \infty)

Solution steps

Find positive values for logs:

x < - 4 or x > 7

Find undefined (singularity) points:

x = 7, x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or x > 7

What is the domain of f(x)=ln(1/((x^2-3x-28))) ?
The domain of f(x)=ln(1/((x^2-3x-28))) is x<-4\lor x>7