Simple log inequality (CAL 1) I am an amateur when it comes to math. I am currently taking CAL 1

broggesy9

broggesy9

Answered question

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(x)=x3x32x and f(x)=ln(g(x)) I have to find the domain of y=f(x) I've figured out that when I do x3x22x>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.

Answer & Explanation

hoppledhsy

hoppledhsy

Beginner2022-05-01Added 13 answers

You need to figure out under what conditions on x is
x3x22x>0. Factoring the lhs we have:
x(x2x2)
which then simplifies to:
x(x2)(x+1)
Thus, you need to identify the set of x for which:
x(x2)(x+1)>0
Can you take it from here?

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