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

Question

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

Let f, g, and h be functions from R  R

Answer 1

I thought James' answers were on target, but if we need functions that are neither bounded below nor bounded above, turn every "^2" into a "^3". So,

f(x)=2x^3+1
g(x)=-x^3+1
h(x)=-x^3+1

Each of these functions is onto the reals, so they aren't bounded in any obvious sense. However, as before, their sum is 3--which is bounded.

Answer 2

James,

Your previous functions would be bounded since the answers would always be positive therefore the max value of one of your given functions is one if the other two are set at their minimums which are one and one. So all of your functions are bounded by one.

Answer 3

let f= 2x^2+1
let g=-x^2+1
let h=-x^2+1
Then f+g+h=3 which is bounded.