What is the domain of f(x)=log_{e}(arcsin(x^2+6x+9)) ?

The domain of f(x)=log_{e}(arcsin(x^2+6x+9)) is -4<= x<-3\lor-3<x<=-2

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domain of f(x)=log_{e}(arcsin(x^2+6x+9))

domain

- 4 \leq x < - 3 or - 3 < x \leq - 2

Interval Notation

[- 4, - 3) \cup (- 3, - 2]

Solution steps

Find positive values for logs:

- 4 \leq x < - 3 or - 3 < x \leq - 2

The function domain

- 4 \leq x < - 3 or - 3 < x \leq - 2

What is the domain of f(x)=log_{e}(arcsin(x^2+6x+9)) ?
The domain of f(x)=log_{e}(arcsin(x^2+6x+9)) is -4<= x<-3\lor-3<x<=-2