Question

If  (x) is a polynomial satisfying (x). (1/x) = (x) + (1/x), and (3) = 28, then f (4) is given by

 

Solution

Correct option is

65

By considering a general nth degree polynomial and writing the

expression  (x). (1/x) = (x) + (1/x) in terms of it, it can be

proved by comparing the coefficients of xxn-1,… and the constant term, that the polynomial satisfying the above equation is either of the form x+1 or –x+ 1. Now, from (3) = 3+1 = 28

We get 3n = 27, or n = 3. But f (3) = –3+1 = 28 is not possible, as –3n= 27 is not true for any value of n. Hence f (4) = 4+ 1 = 65.

SIMILAR QUESTIONS

Q1
Q2

The domain of the function 

Q3

The domain of 

Q4

The domain of definition of the function

                                

Q6

The period of the function (x) = cosec3x + cot 4x is

Q7

Which of the following sets of ordered pairs define a one to one function?

Q9

Let the function f (x) =  

satisfying 

 

Q10

Let