Piecewise function, help proving! I am stuck :(

[Ethanol]

Okay so I have posted the picture of the question.
I am stuck on part a
and this is what I have so far

I know that the function is not continious between x=0 and x=1, but I can't figure out the pattern.
I know 1/3,1/4,/1,5... all lie under x=1.
But if the denominator is not a natural number it is simply squared.
for example;

if x=1/2.5
then f(x) = (1/2.5)^2

there must be a x-value that is not defined though.
Please help!

 

[tkhunny]

Why do you think there is anything undefined?

Your straight line segment between (1,1) and (2,4) is very confusing. Your gaps between the other linear points are also very confusing.

You may wish to start by sketching y = x^2, then simply delete a few points (1/2, 1/4), (1/3, 1/9), etc. and replace them with their linear friends (1/2,1/2),(1/3,1/3), etc.

Think carefully on the definition of continuity. It's probably not continuous where you deleted a point and replaced it with some point somewhere else. Notice how this did not quite happen at (1,1). Think really hard about (0,0).