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3 a. Give an example of a function defined everywhere on the interval $[0,1]$ , which does not achieve its maximum. b. Give an example of a function defined on $mathbb{R}$ , that is nowhere continuous. c. Give an example of a continuous function defined on a bounded set, which is not uniformly continuous. My answers are $f(x) = x^2$ $f(x) = {1$ , if $x$ is rational; $-1$ , if $x$ is irrational $}$ $f(x) = 1/x$ My workings are attached. Please help verify if the working is correct.Solutions real-analysis continuity maxima-minima uniform-continuity share | cite | improve this question asked Dec 1 at 22:36 Ty