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IIT MATH 149 - Math 149 QUIZ 5

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Math 149 – 01 – 03 QUIZ 5 Bonus Points Name:(circle your section)Dr. P. D. McCray Due 9 March, 2012 Page 1 of 3Justify your answers: NO CREDIT for“answers only” !1. (4 points each) Consider a function f given by the formula f.x/ Dx  4p4  x:Be sure to justify each answer!(a) Show that f is invertible.(b) What is the domain of f ? What is the range of f ?(c) Find a formula for the inverse function g of f .(d) What is the domain of g ? What is the range of g ?2. (14 points) Suppose that f1is the inverse of a differentiable function f and let G.x/ D1f1.x/:If f.3/ D 2 and f0.3/ D17; find G0.2/ and explain why your answer is correct. (See 6.1, ex. 46)Math 149 – 01 – 03 QUIZ 5 Bonus Points Name:(circle your section)Dr. P. D. McCray Due 9 March, 2012 Page 2 of 33. (7 points each) (See 6.1, ex. 50.)(a) If f is a one-to-one, twice differentiable function with inverse funcion g, show thatg00.x/ Df00.g.x//Œf0.g.x//3:(b) Explain why if f is increasing and concave upward, then its inverse function g is concave


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IIT MATH 149 - Math 149 QUIZ 5

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