# Thread: Domain Problem and Inverse Problem

1. ## Domain Problem and Inverse Problem

I need a little help here !!!

3) Find the domain of

f(x) = sqrt x / (ln (x^2 + 1) - 17) i don't know how to do this ..please use union

4) Find inverse f(x) = e^x^3 - 2 the -2 is not beside 3 it is beside x....i got cube root 3 of lnx + 2

Thanks

2. ## Re: Domain Problem and Inverse Problem

"Domain" is usally defined in terms of the GREATEST set of values. This makes it most convenient, very often, to consider a very GREAT set of values. Try starting with "All Real Numbers" and see what must be discarded.

ln(x) requires x > 0

sqrt(x) requires x >= 0

1/x requires x <> 0

What say you?

3. ## Re: Domain Problem and Inverse Problem

Originally Posted by qwerty999
I need a little help here !!!

3) Find the domain of

f(x) = sqrt x / (ln (x^2 + 1) - 17) i don't know how to do this ..please use union

4) Find inverse f(x) = e^x^3 - 2 the -2 is not beside 3 it is beside x....i got cube root 3 of lnx + 2

Thanks
Assuming you mean " $f(x)= e^{x^3}}- 2$" and not " $f(x)= (e^x)^3- 2$" which would be more simply written " $f(x)= e^{3x}- 2$", and assuming you mean "cube root of (ln(x+ 2))" and not "cube root of (ln(x)+ 2)" or "cube root of (ln(x))+ 2", yes, that is correct.
Please use parentheses to clarify what you mean!

But what in the world is "cube root 3 of "??? I assume you mean just "cube root". "third root" would mean the same. Never use the unfortunate notation "root 3" or worse "squareroot 3" which I have seen before. Both of those would mean "square root of 3 times...".