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How many real numbers are not in the domain of the function f(x) = (1/x-64)  +  (1/x^2 - 64)  +  (1/x^3 - 64)

 Dec 14, 2021
 #1
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There are 1 + 2 + 3 = 6 real numbers that are not in the domain.

 Dec 14, 2021
 #2
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If the function is:  f(x)  =  1 / (x - 64)  +  1 / (x2 - 64)  +  1 / (x3 - 64)

 

The real solution of  x - 64  is  64

The real solutions of  x2 - 64  are  8  and  -8

The real solution of  x3 - 64  is  4                       (there are also two complex solutions)

 

Thus, there are 4 real numbers not in the domain of this function.

 Dec 15, 2021

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