What is the domain of f(x)=log_{5}(-x^2+7|x|-12) ?

The domain of f(x)=log_{5}(-x^2+7|x|-12) is -4<x<-3\lor 3<x<4

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domain of f(x)=log_{5}(-x^2+7|x|-12)

domain

f (x) = lo g_{5} (- x^{2} + 7 ∣ x ∣ - 12)

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

Interval Notation

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

Solution steps

Find positive values for logs:

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

The function domain

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

f (x) = \frac{x}{( x ^{2} - 1 )}

\frac{x ^{2} + 6 x + 11}{x + 4}

f (x) = 4 - 4 - x^{2}

f (x) = x (x - 3) (x + 5)

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

What is the domain of f(x)=log_{5}(-x^2+7|x|-12) ?
The domain of f(x)=log_{5}(-x^2+7|x|-12) is -4<x<-3\lor 3<x<4