What is the domain of f(x)=(x-4)/(x^2+10x+21) ?

The domain of f(x)=(x-4)/(x^2+10x+21) is x -3

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domain of f(x)=(x-4)/(x^2+10x+21)

domain

f (x) = \frac{x - 4}{x ^{2} + 10 x + 21}

x < - 7 or - 7 < x < - 3 or x > - 3

Interval Notation

(- \infty, - 7) \cup (- 7, - 3) \cup (- 3, \infty)

Solution steps

Find undefined (singularity) points:

x = - 3, x = - 7

The function domain

x < - 7 or - 7 < x < - 3 or x > - 3

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

- 5 + ln (x)

2 x^{3} + x^{2} - 3 x + 1

y = x + 7

(- 1, 2), (1, 6)

What is the domain of f(x)=(x-4)/(x^2+10x+21) ?
The domain of f(x)=(x-4)/(x^2+10x+21) is x<-7\lor-7<x<-3\lor x>-3