Question

if f(x) is a ploynomial function satisfying the condition f(1/x)=f(x)+f(1/x)and f (2) =9 then​

Answer 1

Step-by-step explanation:

The polynomial which satisfies f(x)f(1/x)=f(x)+f(1/x) is ±x  

n

+1 (standard result)

Given that f(2)=9

⇒±2  

n

+1=9

⇒2  

n

=8

(-ve sign not possible here)

⇒n=3

Hence the function is f(x)=x  

3

+1

⇒f(1)=2,f(3)=28,f(5)=126

f(4)=65,f(6)=217