Question: A function h : A -> B is observed to have an inverse function h -1 such that h -1 (x) = x 10 +

A function h : A -> B is observed to have an inverse function h-1 such that

h-1(x) = x10 + x4 + 1 for all x B. Given this information:

(a) Compute h-1(x) for x = 2; 1; 0; -1; -2.

(b) Is it possible that B contains both -1 and 1? If so, give an example of one

possible such set B, and if it is not possible, explain why not.

(c) You are given additional information: h is concave on the interval [1; 3]. Using

this fact, explain why h(2) h(1) + h(3)=2. (We advise not to try to

compute a formula for h(x).)

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