Question

hey..please help on this one.
A function f is continuous at 1 , and it is given that lim ->2 , f(3x-5) - 2/(x-2) = 6 .now I am supposed to find the function f(x). Tried but couldnt figure out. Is it even doable?

Answer 1

alright, we know that lim(xapproaches2) f(3x-5)-2/(x-2)=6, then f(6-5)-2/(2-2)=6 then f(1)=6+2/0=infinity, f(1)=infinity; there are a number of functions which satisfy this coordinate, -ln(x-1) comes to mind.

Answer 2

thanks for answering... I aint sure if i got this right but as you have mentioned that f(1) -> infinity but initially they have given f is continuous at 1 ...so isnt it contradictory...please help

Answer 3

continuity and value are unrelated, as long as the function is differentiatable at that point it can be concluded to be continuous there as well, since d/dx -ln(x-1)=-1/(x-1)= g(x) and g(1)=infinity the original function is continuous just with a vertical slope.

Answer 4

thank you coureges...its making sense now ..although its still a bit diificult for my inner to acccept... one more question..how do i assign you a medal??

Answer 5

I have absolute no idea.

Answer 6

okay..let me play around the website..

Answer 7

anyways thanks..