Posted by Jay on Thursday, November 24, 2011 at 1:38am.
well, we know that f(3) = 5
That means that if 5 = 3f(-x+1) + 2
then f(-x+1) = 1
Hmmm. If x = -2 then we have
y = 3f(3)+2 = 3(5)+2 = 17
Is there more to this problem than you have stated? Is the graph a line, parabola, what?
We do know that 3f(-x+1)+2 is f(x) reflected about the line x=1, scaled by a factor of 3 and shifted up by 2.
Thanks and no, it doesn't state whether or not its a parabola, etc.
f(3) = 5?
isn't x=3 and y=5?
also, how is f(-x+1) = 1 :S did you factor out the negative?
Hmm. good question. I guess I was rambling around ideas, and lost track of what was what.
I think my only relevant comment is about the reflection, scaling, and translation, and even it was a bit off.
If y=f(x)
y = f(x-1) is the same graph shifted one unit to the right.
f(1-x) is that graph reflected about the line x=1
3f(1-x) is the translated, reflected graph scaled by a factor of 3
3f(1-x)+2 is the translated, reflected, scaled graph, shifted up 3 units.
If we call this new function g(x) = 3f(1-x)+2, then we can't evaluate g(3) becauise that is 3f(-2)+2 and we don't know what f(-2) is.
So, are we supposed to find g(-2)? That would be 3f(3)+2 = 17, so I guess you could say that (-2,17) is a "corresponding point".
Are we supposed to find x so that g(x) = 5? If so, that means that 3f(1-x)+2 = 5 and so 3f(1-x) = 3 and so f(1-x) = 1
But we have no idea where f(x) = 1.
I think hyou need to take a look at your course materials to see what they are trying to get at with this problem.