# composition of functions

For the functions f(x)=3x-12 and g(x)=(x/3)+4, find each of the following a) f o g (x) b) g o f (x)

Answers
The way composition works is that you work from right to left. So is you have f o g (x) then do g first, then f, In the same way, g o f means f first, then g. Also you can write f o g(x) = f(g(x)), i.e. in the form of f (here f(x) = 3x - 12, and the 3x -12 bit is what I'm calling the "form"), replace x by g(x). So: f o g (x) = 3g(x) - 12 = 3[x/3 + 4] - 12 = 3x/3 + 12 - 12 = x And similarly: g o f (x) = g(f(x)) = [f(x)]/3 + 4 = (3x - 12)/3 + 4 = 3x/3 - 12/3 + 4 = x - 4 + 4 = x So in both cases you get x back! However you didn't really have to do the working for the last one, because: if you find that, for any two functions f and g, f o g(x) = x, then the two functions are "inverse maps". Which means that when you compose the functions one after the other than you get the same number out as the one you put in. If two maps are inverse maps, then it's always true that the order in which you compose them doesn't matter, and that f o g (x) = g o f (x) = x. Hope this is clear, but if you need more clarifaction let me know.
jim360
23 October 2012
Thank you sooo much this was very clear and i understand it much better now i appreciate you taking out the time to help me abd thank you again
kenya131
23 October 2012
You're welcome. MY post hasn't formatted correctly sadly, but if you could follow it that's all that matters.
jim360
23 October 2012