Reciprocal of a cubic function

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The discussion centers on the possibility of a cubic function having a reciprocal without vertical asymptotes. It concludes that if a reciprocal lacks vertical asymptotes, the cubic function must have no roots, which is impossible. Therefore, all reciprocal functions derived from cubic functions will inherently have vertical asymptotes. This aligns with the mathematical properties of cubic functions and their reciprocals. Ultimately, no cubic function can exist without roots that would prevent vertical asymptotes in its reciprocal.
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Is it possible to have the reciprocal of a cubic function that does not have any vertical asymptotes?
 
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If the reciprocal has no vertical asymptotes, then the cubic function would have no roots. No such cubic exists.
 
Yeah.. thought so. I guess for all reciprocal functions, there will always be a vertical asymptote.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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