anonymous
  • anonymous
How do I find domain and range of f(x,y)=ln(sqrt(1+x^2+y^2)? and what is the boundary of the domain and what type of set is it (open, closed, neither)?
Mathematics
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

amistre64
  • amistre64
the domain will be any combination of x and y values that keep the inside of the ln() greater than zero.
amistre64
  • amistre64
sqrt() needs positive number only...
amistre64
  • amistre64
separate it into 2 functions and define the domains of each function: f(u) = ln(u) and g(x) = sqrt(1+x^2+y^2) are we to assume that y is an implicit funtion of x? or an independant variable?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
regardless, sqrt() has to have a domain that is greater than zero for the function to operate inside of normal parameters. Any of this makeing sense?
anonymous
  • anonymous
yes
amistre64
  • amistre64
Since x and y are both squared, anything we use for them will either be a zero or a positive number; which makes sqrt(?) always equal to or greater than 1 which is fine. any values can be used so the domian is (-inf,inf)
amistre64
  • amistre64
since the range is controled by the ln(?) function, it will spit out everything from ln(1)and up....
amistre64
  • amistre64
ln(1) = 0 right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
then the range; the output of this thing; will be from zero to infinity [0,inf)
amistre64
  • amistre64
open or closed just depends on their definitions.... which i am not too certain about :) I mean, open means without bounds, but does a onesided infinity count?
anonymous
  • anonymous
yeah i think it does
amistre64
  • amistre64
double check that and you should have your answers :)
anonymous
  • anonymous
thank you so much!

Looking for something else?

Not the answer you are looking for? Search for more explanations.