I really hope that you have attempted it by hard. Here is my solution, hope you can get some ideas after seeing through it. Good luck!

I finally got it after thinking through it many times for several days , with the help of you guys of course . I am proud to say that I got it without the help of a teacher , but a handful of people on the internet .

If we map the value , or expression of k(x) into the function hk(x) , then we're essentially mapping it to make it a much more complex function , but we're looking for h(x) . So , to get h(x) , we inverse k(x) to find x [ if we inverse k(x) , we're finding the initial object - x ] . Hence , after finding it , we can determine h(x) . I tried checking by substitution and finding the inverse in many ways , and found out that it is indeed the case . Then , we're writing it as h(y) because it's just an arbitrarily chosen letter , a place holder since we cannot have a function that is defined as h(x) = y-6 or etc ... So after solving it , we revert it back to h(x) - x-6 .

It's exhilarating finally understanding a concept . None of the seniors in my school managed to explain it to me .

Now , can we find the inverse of a composition of function , say gf(x) ? If yes then I'll get f(x) which will further reinforce my understanding of the concept .

This post has been edited by maximR: Jan 19 2012, 07:20 PM