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(a) Let  f(x): (-inf, 0) U (0 inf) --> R be defined by f(x) = x- (1/x)
Show that f(x) has no inverse function.

(b) Let g(x): (), inf) --> R be defined by gx) = x- (1/x)
Show that g(x) has an inverse function.

 

I don't understand this. Please help!

 
 Nov 22, 2020
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If you graph y = x - 1/x, then it clearly fails the Horizontal Line Test over all real numbers, so f is not invertible.  But if you restrict to positive real numbers, then it passes the Horizontal LIne Test, so g is invertible.

 
 Nov 23, 2020

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