broggesy9

2022-04-30

Simple log inequality (CAL 1)

I am an amateur when it comes to math. I am currently taking CAL 1 and have a question about one of my assignments. Any help is appreciated.

Let$g\left(x\right)={x}^{3}-{x}^{3}-2x$ and $f\left(x\right)=\mathrm{ln}\left(g\left(x\right)\right)$ I have to find the domain of $y=f\left(x\right)$ I've figured out that when I do ${x}^{3}-{x}^{2}-2x>0$ I end up with $0,2,-1.$

But I'm still not sure what the domain is.... maybe I'm close? maybe it's obvious? Any help much appreciated!!!

Thanks.

I am an amateur when it comes to math. I am currently taking CAL 1 and have a question about one of my assignments. Any help is appreciated.

Let

But I'm still not sure what the domain is.... maybe I'm close? maybe it's obvious? Any help much appreciated!!!

Thanks.

hoppledhsy

Beginner2022-05-01Added 13 answers

You need to figure out under what conditions on x is

${x}^{3}-{x}^{2}-2x>0$ . Factoring the lhs we have:

$x({x}^{2}-x-2)$

which then simplifies to:

$x(x-2)(x+1)$

Thus, you need to identify the set of x for which:

$x(x-2)(x+1)>0$

Can you take it from here?

which then simplifies to:

Thus, you need to identify the set of x for which:

Can you take it from here?

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