What is the domain of f(x)=(x-6)/((x-5)(x+4)) ?

The domain of f(x)=(x-6)/((x-5)(x+4)) is x 5

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domain of f(x)=(x-6)/((x-5)(x+4))

domain

f (x) = \frac{x - 6}{( x - 5 ) ( x + 4 )}

x < - 4 or - 4 < x < 5 or x > 5

Interval Notation

(- \infty, - 4) \cup (- 4, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5, x = - 4

The function domain

x < - 4 or - 4 < x < 5 or x > 5

m = - \frac{3}{2}, (- 3, - 3)

x 16 - x^{2}

f (x) = x^{2} - 8 x + 10

f (x) = x^{2} \cdot e^{- 2 x}

- 5 cos (2 π x + 1)

What is the domain of f(x)=(x-6)/((x-5)(x+4)) ?
The domain of f(x)=(x-6)/((x-5)(x+4)) is x<-4\lor-4<x<5\lor x>5