F : {0, 1} 3 → {0, 1} 4 . The output of f is obtained by copying the first bit and adding (concatenating) it to the end of the string. For example, f(011) = 0110 and f(101) = 1011.
(a) Is f one-to-one? Justify your answer.
(b) Is f onto? Justify your answer.
(c) Determine the range of the function

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?

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