What is the domain of f(x)=(ln(x^2-4))/(2x^2+x-15) ?

The domain of f(x)=(ln(x^2-4))/(2x^2+x-15) is x 5/2

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domain of f(x)=(ln(x^2-4))/(2x^2+x-15)

domain

f (x) = \frac{ln ( x ^{2} - 4 )}{2 x ^{2} + x - 15}

x < - 3 or - 3 < x < - 2 or 2 < x < \frac{5}{2} or x > \frac{5}{2}

Interval Notation

(- \infty, - 3) \cup (- 3, - 2) \cup (2, \frac{5}{2}) \cup (\frac{5}{2}, \infty)

Solution steps

Find positive values for logs:

x < - 2 or x > 2

Find undefined (singularity) points:

x = \frac{5}{2}, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x < - 2 or 2 < x < \frac{5}{2} or x > \frac{5}{2}

(- 1, - 2), (2, 4)

(x + 3)^{3} - 1

f (x) = (x - 3) x

f (x) = 2 x^{2} + 3 x - 4

f (x) = 1 - ∣ x ∣

What is the domain of f(x)=(ln(x^2-4))/(2x^2+x-15) ?
The domain of f(x)=(ln(x^2-4))/(2x^2+x-15) is x<-3\lor-3<x<-2\lor 2<x< 5/2 \lor x> 5/2