a) Show that v (x-y)^2 = |x-y| where |z| is the absolute value of z. Provide an example to show that v (x-y)^2 is ? x-y.b) Does f(x) = vx whose domain is the non-negative reals satisfy:
i. property A?
ii. property B?
c) Provide an example of a function that satisfies:
i. properties A and B.
ii. neither property A nor B.
3. Consider two properties that a function f might satisfy: (A) for all strictly positive real numbers e there exists a strictly positive real number d such that Vxy in the domain of f (B) Vxy in the domain of l there exists a finite constant c ~ 0 such that Ju (x) -f {y))2 ::;cJ{x _ y)2 (a) Show that Jex -y)2 = Ix -yl where Izl is the absolute value of z. Provide an example to show that J(x -y)2 =1= x -y. (Hint: it will later be useful to remember that [z]

Attachments: