What is the domain of f(x)=(-x^2+9x+1)/(2x^2+14x+24) ?

The domain of f(x)=(-x^2+9x+1)/(2x^2+14x+24) is x -3

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domain of f(x)=(-x^2+9x+1)/(2x^2+14x+24)

domain

f (x) = \frac{- x ^{2} + 9 x + 1}{2 x ^{2} + 14 x + 24}

x < - 4 or - 4 < x < - 3 or x > - 3

Interval Notation

(- \infty, - 4) \cup (- 4, - 3) \cup (- 3, \infty)

Solution steps

Find undefined (singularity) points:

x = - 3, x = - 4

The function domain

x < - 4 or - 4 < x < - 3 or x > - 3

- 8

lo g_{a} (x)

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

f (x) = - \frac{9}{2 t ^{(\frac{3}{2})}}

f (x) = e^{- x}

What is the domain of f(x)=(-x^2+9x+1)/(2x^2+14x+24) ?
The domain of f(x)=(-x^2+9x+1)/(2x^2+14x+24) is x<-4\lor-4<x<-3\lor x>-3