f(x)=ln(x)+e^(1/x-1). What´s the domain for f?

Any suggestions on where to start? :)

Question

f(x)=ln(x)+e^(1/x-1). What´s the domain for f?

Any suggestions on where to start? :)

anonymous · Answer

since the function f(x) has two distinct parts, you should start with them and then find the intersection of the two individual domains, like for Ln(x) the domain would be_

amistre64 · Answer

*union of them

zzr0ck3r · Answer

You have two things to worry about $x>0$ because of the domain of $\ln(x)$ and $x-1\ne 0$ because of the $\dfrac{1}{x-1}$ (we cant divide by $0$).

So we can use all positive numbers except $1$.

Domain is $\{x\mid x>0\text{ and } x\ne 1\}=(0,1)\cup (1,\infty)$


Make sense?

amistre64 · Answer

hmm, might be looking at it in a mirror tho ... the union of the bad parts that is

anonymous · Answer

Yes, it makes totally sense! Thanks!

zzr0ck3r · Answer

np

zzr0ck3r · Answer

I think we want the intersection of the two @amistre64

anonymous · Answer

np? :)

zzr0ck3r · Answer

no problem @Wikis

anonymous · Answer

Of course XD Thought it was a math term that I had missed :D

amistre64 · Answer

intersection of the domains yes ... i was thinking about the exclusions at first.  we want to make sure all the bad parts are avoided for each term

amistre64 · Answer

if x=2,3 are bad for the first part, and  x=2,4,5 are bad for the last part; then we would exclude x=2,3,4,5 was in my head

amistre64 · Answer

time to build a house ... have fun