3) Consider the function g(x) given by y = 9-3x². a) Is g one-to-one on R? Be able to explain briefly why or why not. b) Does the inverse function y = g-¹(x) exist in the neighborhood of the point xº = 2? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x = = c) Does the inverse function y = 9-¹(x) exist in the neighborhood of the point x* = 0? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x=x*. 4) Let z = [e] = e.) e²(-¹) and x = €²(x-4) x-3 =y-y²+4. Calculate dz/dy and evaluate it at y = 1. (Note that

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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3) Consider the function g(x) given by y = 9-3x².
a) Is g one-to-one on R? Be able to explain briefly why or why not.
b) Does the inverse function y = g-¹(x) exist in the neighborhood of the point xº = 2?
(Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at
x = =
c) Does the inverse function y = 9-¹(x) exist in the neighborhood of the point x* = 0?
(Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at
x=x*.
4) Let z = e²(-¹) and x =
[ex] = e.)
x-3
=y-y²+4. Calculate dz/dy and evaluate it at y = 1. (Note that
Transcribed Image Text:3) Consider the function g(x) given by y = 9-3x². a) Is g one-to-one on R? Be able to explain briefly why or why not. b) Does the inverse function y = g-¹(x) exist in the neighborhood of the point xº = 2? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x = = c) Does the inverse function y = 9-¹(x) exist in the neighborhood of the point x* = 0? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x=x*. 4) Let z = e²(-¹) and x = [ex] = e.) x-3 =y-y²+4. Calculate dz/dy and evaluate it at y = 1. (Note that
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