On what domain and codomain would the log() function be one-to-one and onto?

Question

shubhamsrg · Answer

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you should know the domain and co-domain from this graph i guess..

anonymous · Answer

What I did is just make the domain and codomain x-->x, found the inverse of $$y=logx$$ and by definition, if a function is invertible it is both onto and one-to-one

shubhamsrg · Answer

you need to find the domain and co-domain right for which it is one one
as you can see,,for every x in the graph,y has a unique value, hence its always one one in its domain..
you just have to mention its domain and codomain..
did i explain well?

anonymous · Answer

so are you saying that the domain and co domain are x>0?

shubhamsrg · Answer

domain is x>0 yes..

co-domain will be the permissible values of y.

anonymous · Answer

y is an element of the reals?

shubhamsrg · Answer

yep..you got it
x>0 and y all real numbers!
bingo! :)

anonymous · Answer

Thanks

shubhamsrg · Answer

glad to help :)