What is the domain of f(x)=(2-x^2)/(x^2+6x-40) ?

The domain of f(x)=(2-x^2)/(x^2+6x-40) is x 4

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domain of f(x)=(2-x^2)/(x^2+6x-40)

domain

f (x) = \frac{2 - x ^{2}}{x ^{2} + 6 x - 40}

x < - 10 or - 10 < x < 4 or x > 4

Interval Notation

(- \infty, - 10) \cup (- 10, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = - 10

The function domain

x < - 10 or - 10 < x < 4 or x > 4

g (x) = - x + 1

x^{2} - 6 x + 10

x

f (x) = e^{x}

What is the domain of f(x)=(2-x^2)/(x^2+6x-40) ?
The domain of f(x)=(2-x^2)/(x^2+6x-40) is x<-10\lor-10<x<4\lor x>4