function concept

[pasami]

If f(x+(1/x)) = x^2 + (1/x)^2
What is the value of f(x)?

A. x^2 + 1
B. x + (1/x)
C. x^2 - 2
D. x^2 + 2
E. x^2 + 2x

[HSPA]

IMO C

[Anurag@Gurome]

If f(x+(1/x)) = x^2 + (1/x)^2
What is the value of f(x)?

For x = 1, f(1 + (1/1)) = 1^2 + (1/1)^2 ----> f(2) = 2

Hence, the correct option must give f(2) = 2.
Let us check them one by one,

• A. f(2) = 2^2 + 1 = 5 ----> NO
  B. f(2) = 2 + 1/2 = 2.5 --> NO
  C. f(2) = 2^2 - 2 = 2 ----> YES
  D. f(2) = 2^2 + 2 = 6 ----> NO
  E. f(2) = 2^2 + 2*2 = 8 --> NO

The correct answer is C.

[HSPA]

add 2 and substract 2 ..this can also do the trick. We can write 2 = 2 *x * (1/x) and we get (a+b)^2

[pasami]

f(x + (1/x)) = x^2 + (1/x)^2
= x^2 + (1/x)^2 + 2*x*(1/x) - 2*x*(1/x)
= (x + (1/x))^2 - 2

Replace (x + (1/x)) by say 't', the equation becomes

f(t) = t^2 - 2
or f(x) = x^2 - 2

So answer is 'C'.