What is the domain of f(x)=(4x^2-36)/(x^2-2x-8) ?

The domain of f(x)=(4x^2-36)/(x^2-2x-8) is x 4

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domain of f(x)=(4x^2-36)/(x^2-2x-8)

domain

f (x) = \frac{4 x ^{2} - 36}{x ^{2} - 2 x - 8}

x < - 2 or - 2 < x < 4 or x > 4

Interval Notation

(- \infty, - 2) \cup (- 2, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = - 2

The function domain

x < - 2 or - 2 < x < 4 or x > 4

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

f (x) = \frac{x - 4}{x ^{2} + 9}

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

\frac{2 x + 3}{3 x - 4}

f (x) = \frac{x - 4}{x + 7}

What is the domain of f(x)=(4x^2-36)/(x^2-2x-8) ?
The domain of f(x)=(4x^2-36)/(x^2-2x-8) is x<-2\lor-2<x<4\lor x>4