# Homework Help: Bounded functions

1. Aug 25, 2010

### WackStr

1. The problem statement, all variables and given/known data

This is from baby rudin:

If $$E\subset X$$ and if f is a function defined on X, the restriction of f to E is the function g whose domain of definition is E, such that $$g(p)=f(p)$$ for $$p\in E$$. Define f and g on R^2 by: $$f(0,0)=g(0,0)=0$$, $$f(x,y)=\frac{xy^2}{x^2+y^4}, g(x,y)=\frac{xy^2}{x^2+y^6}$$ if $$(x,y)\neq (0,0)$$. Prove that f is bounded on R^2, that g is unbounded in every neighborhood of $$(0,0)$$, and that f is not continuous at (0,0); nevertheless, the restrictions of both f and g to every straight line in R^2 are continuous.

2. Relevant equations

In the question statement

3. The attempt at a solution

This is after the continuity chapter and before the differentiation chapter, so I am clueless here. I was thinking of bounding the function by another function but didn't get anywhere. Anyone wanna help?

Thanks,
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution