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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) + 1/(x^4 - 64)

 Apr 27, 2021
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The real numbers that are not in the domain of the function f(x)=(1x−64)+(1x2−64)+(1x3−64)f(x)=(1x−64)+(1x2−64)+(1x3−64) are the numbers that will make the function undefined.

We look at the fraction denominators. The function will be undefined when either of the denominators is equal to zero.

Case 1:

x−64=0x−64=0

Add 64 to both sides and simplify:

x−64+64=0+64⟹x=64x−64+64=0+64⟹x=64

Case 2:

x2−64=0x2−64+64=0+64x2=64⟹x=±√64∴x=8,x=−8x2−64=0x2−64+64=0+64x2=64⟹x=±64∴x=8,x=−8

Case 3:

x3−64=0x3−64+64=0+64x3=64⟹x=3√64∴x=4x3−64=0x3−64+64=0+64x3=64⟹x=643∴x=4

Hence the real numbers that are not in the domain of the given function are −8,4,8−8,4,8 and 64

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 Apr 27, 2021

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