The discussion revolves around finding a function f(x) that satisfies the equation 3f(x) + f(3-x) = x squared. Participants are exploring various substitutions and manipulations of the equation to derive f(x).
The discussion is ongoing, with participants sharing their attempts and questioning the validity of their approaches. Some guidance has been offered regarding how to isolate f(x) using the derived equations, but there is no consensus on the next steps or the final form of f(x).
Participants are grappling with the implications of their substitutions and the resulting equations, indicating a need for clarity on the relationships between the variables involved. There is also mention of potential confusion arising from the nature of the substitutions being discussed.
OTHER EDIT!pugfug90 said:I first tried replacing "x" when in parenthese with y. Therefor, 3y+3-y=x, yadda yadda, 2y=x-3, y=(x-3)/2, however, the real answer turned out to be some weird fractional thing. Please give me some kind of direction..
pugfug90 said:3f(3-x)+f(x)=3-x is what I get if I plug in 3-x where x is...
pugfug90 said:Oops haha
So 3f(3-x)+f(x)=(x squared)+9-6x.
So can you tell me where to go from here? I tried substituting y into x again, get (x squared - 6x)/-2, while the real answer is something like x/3+x/5-3 or something. Also, where did the 'plug 3-x for x everywhere' thing came from? And if this is a "topic" I can look up like for quadratic equations, or "f and g compositions"?
He said substitute for, not set equal to.qspeechc said:I am sorry, I was just reading through this thread: how can you substitute x for x-3? Doesn't this imply -3=0?