3. A function h: A B is observed to have an inverse function h such that...

 

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3. A function h: A B is observed to have an inverse function h such that h(x) = x10x4+1 for all x B. Given this information: (a) Compute h (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 you not to try to compute a formula for h(x).) 3. A function h: A B is observed to have an inverse function h such that h(x) = x10x4+1 for all x B. Given this information: (a) Compute h (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 you not to try to compute a formula for h(x).)

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a To compute hx for various values of x we start with the equation hh1x x and sol... View the full answer