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= (-)e, + x,2e, satisfies the conditions of the inverse function theorem for 7.51. Show that f(x) all x except * = 0 but is not 1-1 on this set. ohos olo tgeono 8 Show that the function

= (-)e, + x,2e, satisfies the conditions of the inverse function theorem for 7.51. Show that f(x) all x except * = 0 but is not 1-1 on this set. ohos olo tgeono 8 Show that the function

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please note that a bold letter indicates a vector and that this problem involves a vector function of a vector variable.

= (-)e, + x,2e, satisfies the conditions of the inverse function theorem for 7.51. Show that f(x) all x except * = 0 but is not 1-1 on this set. ohos olo tgeono 8 Show that the function
Transcribed Image Text:= (-)e, + x,2e, satisfies the conditions of the inverse function theorem for 7.51. Show that f(x) all x except * = 0 but is not 1-1 on this set. ohos olo tgeono 8 Show that the function
Expert Solution
Step 1

Function is given as,

f(x)(xxe xx,e
Step 2

Inverse function theorem:

Let, any mapf : R" -> R" is continously differentiable on some open set which contains a, and consider Jf(a #0. Then there exist some open set V containing a and an open set W which contains f(a)such that f :V ->W has a continuous inverse f1 WVwhich is differentiable Vy e W
Step 3

Given function can be written as,

f(x) (x) - x2 e1 е, f(x) е х,х, е, Where, f(xx-x,'. f(x)= x,x, and x|
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