IF F( X) IS A POLYNOMIAL FUNCTION SATISFYING F(X)*F(1/X)=F(X) + F(1/X),AND F(3)=28 ,THEN F(4) IS EQUAL TO
A.63
B.65
C.68
D.67

If f(x) ×f(1x)=f(x)+f(1x),thenf(x)=1±xnNow,f(3)=281+3n=28  or 1-3n=283n=27  or  3n=-27 ( not possible)n=3f(x)=1+x3f(4)=1+43=65

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f(x)*f(1/x) = f(x) + f(1/x) is satisfied by the function f(x) = 1 + xk .
Given: f(3) = 28
          i.e 1 + 3k  = 28
          i.e 3k  = 27
          or k = 3.
 So, f(x) = 1 + x3 .
    Now, f(4) = 1 + 43  = 65
  Option b).
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