Hello there . I'm currently having a problem with a composite functions question . I know how to solve it , but have no idea as to why I should express y in terms of x before solving it . To get an idea , I've posted the question with a solution :



Why can't I just plug in x+4 in the expression x^2+8x+10 ? Why should I express the function f(x) = y first , and then express y in terms of x ?

This post has been edited by maximR: Jan 15 2012, 07:07 PM

Hi . Never knew I'll get so many great responses . Anyway , yes , I finally got to the point that I can't understand the concept from all the reference books available , and also the textbooks . Since I'm currently tuition-less , I'll have to resort to asking on the internet , and I've gotten great responses .

From all of the posts above , I figured I'll simplify the main gist of the concept , at least for me :

We're finding h(x) , but if we map k(x) to the function x^2+8x+10 , I'll get the value of hk(x) instead and not h(x) . And to find x from k(x) , we'll have to inverse it , by letting y as the subject and then from there , express x in terms of y .

Since y is set to be equal to k(x) , which is x+4 , to solve for x , it will be x=y-4 .

But then when it comes to here my logic and reasoning doesn't understand this part : SINCE y=x+4 , and x=y-4 , why do we say its h(y) instead and not h(x) ? Is y=y-4 ?

If this is true , that we must express x in terms of y to get the same-object-criteria , then I get it . But shouldn't the right equation be named the image instead ?

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Added on January 17, 2012, 6:33 pmI'm really tired , and after seeing it for a few times I still couldn't get it . I'm really too tired , back from merentas desa . I'll look at it again tomorrow and PM you about it .\

p/s : Pretty close . I'm about to get it .

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Added on January 17, 2012, 6:34 pmI need guidance for number 9 and 10 .

This post has been edited by maximR: Jan 17 2012, 06:37 PM

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