1how to draw the graph of such function?
5 Answers
1357try to draw graphs of function
f(x)=x for all real numbers
f(x)=1-x for all real numbers
and try to think on the question
1For any rational number k : f(k) = k
Take any irrational number k+h which is very close to k meaning h tends to 0 but is irrational
f(k+h) = 1-k-h
for f(x) to be continuous : f(k)=f(k+h)
k=1-k-h
k = 0.5 (after neglecting h)
so f(x) is discontinuous at all rational values of x except x = 0.5