# F(f(x))= (x^4)-4(x^2)+2, find f(x).

1. Oct 13, 2013

### GreenTea09

1. The problem statement, all variables and given/known data
http://postimg.org/image/48919pl1x/

2. Relevant equations
f(f(x))= (x^4)-4(x^2)+2,

3. The attempt at a solution
[f(x)]^2=
(x^4)-4(x^2)+2=
[(x-2)^2]-(4x^2)+2

i cant seem to square root (x^4)-4(x^2)+2...

2. Oct 13, 2013

### Saitama

The question states that f(x) is a polynomial. Use this.

http://en.wikipedia.org/wiki/Polynomial

3. Oct 13, 2013

### GreenTea09

ok,i tried this solution
let f(x)=a(x^2)+bx+c
(a(x^2)+bx+c)*(a(x^2)+bx+c) =(x^4)-4(x^2)+2

comparing the coefficient of x^2
2c+b^2=-4 ---eqn(2)
comparing the coefficient of constant,
i get a c value of sqrt2 and -sqrt2
which i try to fit into eqn(2) but dosent work out..

4. Oct 13, 2013

### arildno

f(f(x)) must also be evaluated on the bf(x)+c terms!!

5. Oct 13, 2013

### Staff: Mentor

The image link is broken.
No one else pointed this out, so I will. f(f(x)) is not the same as [f(x)]2.
That's not relevant here, since you are not being asked to solve for f(x) in the equation [f(x)]2 = ...

What you're working with is a composite of f with itself -- (f o f)(x) --, not the square of f(x).