Question

If f(x) is a polynomial satisfying f(x).F(1x)=f(x)+f(1x) and f(3)=28, then f(4) is equal to:

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

Answer: 65

Step-by-step explanation:

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.