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How many real numbers are not in the domain of the function $$f(x) = \frac{1}{x-64} + \frac{1}{x^2-64} + \frac{1}{x^3-64}~?$$

 Nov 8, 2014

Best Answer 

 #1
avatar+130511 
+8

We only need to be concerned with things that make the denominators = 0

In the first fraction, x = 64 makes the denominator = 0

In the second, setting the denominator = 0, we have....  x^2 - 64 = 0.......factoring, we have (x - 8)(x + 8) = 0

Setting each factor to 0, gives us x =8 and x = -8......and these are the two values that make the denominator = 0

In the third fraction....setting the denominator = 0 fgives us  x^3 - 64 = 0....add 64 to both sides

x^3 = 64.....take the cube root of both sides and we find that  x = 4

So 64, -8,  8 and 4 are not in the domain of the function.

 

 Nov 8, 2014
 #1
avatar+130511 
+8
Best Answer

We only need to be concerned with things that make the denominators = 0

In the first fraction, x = 64 makes the denominator = 0

In the second, setting the denominator = 0, we have....  x^2 - 64 = 0.......factoring, we have (x - 8)(x + 8) = 0

Setting each factor to 0, gives us x =8 and x = -8......and these are the two values that make the denominator = 0

In the third fraction....setting the denominator = 0 fgives us  x^3 - 64 = 0....add 64 to both sides

x^3 = 64.....take the cube root of both sides and we find that  x = 4

So 64, -8,  8 and 4 are not in the domain of the function.

 

CPhill Nov 8, 2014

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