Question 1208085
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Determine if each function is even, odd or neither.

A. F(x) = (x)^(1/3) + |x|^2

B. G(x) = (1/x) - (x)^(1/4)

C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9)

D. S(x) = (x^4 + |x - 4|)/(x^4 - 2x)
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                I will answer  (B),  (C)  and  (D).



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(B)  In (B),  (x)^(1/4)  is defined only for  x >= 0.

     Therefore, function G(x) is defined only for  x >= 0.

     Therefore, the conception of even and/or odd function is inapplicable for G(x).

     Therefore, the answer for (B) is "neither".



(C)  In (C),  (x)^(1/2)  is defined only for  x >= 0.

     Therefore, function H(x) is defined only for  x >= 0.

     Therefore, the conception of even and/or odd function is inapplicable for H(x).

     Therefore, the answer for (C) is "neither".



(D)  In (D), calculate  S(x) at two values of x: x= 1 and x= -1.


     At x= 1,  S(1)  = {{{(1^4+abs(1-4))/(1^4-2*1)}}} = {{{(1+3)/(1-2)}}} = {{{4/(-1)}}} = -4.


     At x= -1, S(-1) = {{{((-1)^4+abs(-1-4))/((-1)^4-2*(-1))}}} = {{{(1+5)/(1+2)}}} = {{{6/3}}} = 2.


     So, neither  S(1) = S(-1)  nor  S(1) = -S(-1).  Thus we conclude that function S(x) is neither even nor odd.
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Parts &nbsp;(B), &nbsp;(C) &nbsp;and &nbsp;(D) &nbsp;are solved and answered, &nbsp;with explanations.