bound/unbounded
1. What is an example of f + g + h being bounded while f, g, and h being unbounded.
2. What about f*g*h being bounded while f,g, and h are unbounded.
Let f, g, and h be functions from R -> R.
1. Something like f=2x^3-1, g=-x^3+1, h=-x^3+1.... together = 3.... but there's got to be something simpler.
2. I originally thought f=x, g=x, h=1/x^2... but that wont work when x=0... so I'm not sure about that one?
2. What about f*g*h being bounded while f,g, and h are unbounded.
Let f, g, and h be functions from R -> R.
1. Something like f=2x^3-1, g=-x^3+1, h=-x^3+1.... together = 3.... but there's got to be something simpler.
2. I originally thought f=x, g=x, h=1/x^2... but that wont work when x=0... so I'm not sure about that one?