functions 'f of g' composition functions?

Question

An assignment for this distance-education class is asking me to do some composition functions that make no sense! I'm honestly wondering is this a typo or if I it is a concept that I don't understand. My question is: Do these questions make sense? Or is there a typo?

I did a screen shot and posted them here:
http://sudokupuzzles.net/rrr.gif

Answer 1

They're asking you to give a function that makes the given function a composite function. For instance, in the first question, you want to create a g(x) so that f(g(x))=F(x), and in the second question you want to create an f(t) so that f(g(t))=u(t). Basically, the question is asking you to think about function composition in the same way that elementary algebra asks you to think about multiplication in questions like "find an x such that 3x=12."

Answer 2

right here's a thank you to construct such an occasion: permit f(x) = x/2 the place the area of f is the unit era. So this style of f is purely [0,a million/2] permit g(x) = x for x in [0,a million/2] and a million-x for x in [a million/2,a million] Intuitively f shrinks and g folds. you may build many greater examples of this style.

Answer 3

regentsprep.org/Regents/mathb/f/compositionfunctions.htm
mathforum.org/library/drmath/sets/select/dm_func_composition.html
en.wikipedia.org/wiki/Function_composition
www-groups.dcs.st-and.ac.uk/CIRCA/Preprints/genfunctions.pdf
math.ucsd.edu/~wgarner/math4c/textbook/chapter2/combfunctions.htm