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Find the inverse function of this piecewise function... (1 Viewer)

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There will be no inverse function for y=0 since you'll have x=0 which is a vertical line (doesn't satisfy function requirement since it has infinitely many y for x=0). Inverse of y=x is x=y, so y=x for x<0. Your domains don't really work. You have an overlap.
 
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I guess in this situation it is fine, but usually we should be exclusive about the domains on which such functions are defined.
 

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