What is the domain of f(x)=(x^2+4x)/(5x^2+36x+64) ?

The domain of f(x)=(x^2+4x)/(5x^2+36x+64) is x -16/5

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domain of f(x)=(x^2+4x)/(5x^2+36x+64)

domain

f (x) = \frac{x ^{2} + 4 x}{5 x ^{2} + 36 x + 64}

x < - 4 or - 4 < x < - \frac{16}{5} or x > - \frac{16}{5}

Interval Notation

(- \infty, - 4) \cup (- 4, - \frac{16}{5}) \cup (- \frac{16}{5}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{16}{5}, x = - 4

The function domain

x < - 4 or - 4 < x < - \frac{16}{5} or x > - \frac{16}{5}

f (x) = x^{2} + 2 x + 6

f (x) = x^{2} + 2 x + 9

y = \frac{x}{x - 2} + x - 1

f (y) = - 3 y - 2

2 x + 20

What is the domain of f(x)=(x^2+4x)/(5x^2+36x+64) ?
The domain of f(x)=(x^2+4x)/(5x^2+36x+64) is x<-4\lor-4<x<-16/5 \lor x>-16/5