bound/unbounded

[robiewiliamsfan]

1. What is an example of f + g + h being bounded while f, g, and h being unbounded

Comments

[pyrop]

There's nothing stopping you from defining h in the 2nd problem to be some arbitrary finite number at x=0.

[bewlay_brother]

Indeed, the functions need only be unbounded, not continuous.

[polynomial]

Maybe I'm confused, but for #1, what about f = 2x, g = -x, and h = -x?

For #2, you can fix things misbehaving at 0 with exponential functions, I think. For example, f = g = 2^x, g = 2^{-2x}?

[squeegibo]

1. As polynomial said, f = 2x, g = -x, h = -x is a solution.
2. f = e^2x, g = e^-x, h = e^-x should work.

[taral]

Cute transform. I missed the second part of his question.

[bewlay_brother]

Remember kids, the exponential function is a group homomorphism between the additive and multiplicative groups of the reals!

[polynomial]

Remember kids, the exponential

There's only one?