F(x).F(1/x)=F(x)+F(1/x) and F(3)=28 then find the value of F(4)

Question

Function topic 

Answer 1

Note that 28 = 3³+1

 

So, Let's try F(x) = x³+1

 

Then F(x)·F(1/x) = [x³+1][(1/x)³+1]

 

                         = 1 + x³ + (1/x)³ + 1

 

                         = (1+x³) + ((1/x)³+1) = F(x) + F(1/x)

 

So, F(x) = x³ + 1 satisfies the given property.

 

For this function, F(4) = 4³ + 1 = 65.

 

Answer 2

Hmmm...

 

How about 

 

F(3) = 3^3 + 3(1/3)= 28

 

F(4) = 4^4 + 4(1/4) = 256 + 1 = 257