-LSB- math -RSB- x ^ 2 < \ frac -LCB- 1 -RCB- -LCB- 100 -RCB- -LSB- / math -RSB- , and -LSB- math -RSB- x < 0 -LSB- / math -RSB- . What is the tightest range in which -LSB- math -RSB- x -LSB- / math -RSB- can lie ?
If a function -LSB- math -RSB- f -LRB- x -RRB- -LSB- / math -RSB- is defined as f -LSB- math -RSB- -LRB- x -RRB- = x -LRB- 1-x -RRB- -LSB- / math -RSB- for -LSB- math -RSB- x -LSB- / math -RSB- rational and -LSB- math -RSB- f -LRB- x -RRB- = \ frac -LCB- 1 -RCB- -LCB- 4 -RCB- - x -LRB- 1-x -RRB- -LSB- / math -RSB- for irrational -LSB- math -RSB- x , -LSB- / math -RSB- what can be said of the continuity of -LSB- math -RSB- f -LRB- x -RRB- -LSB- / math -RSB- in -LSB- math -RSB- -LSB- 0,1 -RSB- ? -LSB- / math -RSB-