Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function g: [cos (1/2)*exp(1/2), cos (1/2)*exp(1/2)]-[-1/2 ,1/2] such that V-1/2 sxs 1/2: g(f(x)) =x. How can I compute g'(1) and g"(1)?|

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function
g: [cos (1/2)*exp(1/2), cos (1/2)*exp(1/2)]-[-1/2 ,1/2] such that
V-1/2 sxs 1/2:
g(f(x)) =x.
How can I compute g'(1) and g"(1)?|
Transcribed Image Text:Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function g: [cos (1/2)*exp(1/2), cos (1/2)*exp(1/2)]-[-1/2 ,1/2] such that V-1/2 sxs 1/2: g(f(x)) =x. How can I compute g'(1) and g"(1)?|
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