Thread: Polynomial Funtion HELP PLEASE!!!

Let f(x) be a polynomial function such that, for all real x.

f(x^2 +2) = x^4 + 10x^2 + 4.

Evaluate f(x^2 - 2).


THANKS FOR YOUR HELP!!!!!!

Originally Posted by rlarach

Let f(x) be a polynomial function such that, for all real x.

f(x^2 +2) = x^4 + 10x^2 + 4.

Evaluate f(x^2 - 2).


THANKS FOR YOUR HELP!!!!!!

Well, the "brute force" method would be:


Let .

Solve for x:




Ignoring the difficulty of the let's blithely continue:




Now let .





which you can expand, or not, as you choose.

-Dan

Originally Posted by rlarach

Let f(x) be a polynomial function such that, for all real x.

f(x^2 +2) = x^4 + 10x^2 + 4.

Evaluate f(x^2 - 2).


THANKS FOR YOUR HELP!!!!!!

RonL

How Do You Get X^2 + 6x - 12

Originally Posted by rlarach

How Do You Get X^2 + 6x - 12

By inspection, the required function is obviously a quadraic with leading
coefficient 1, so is of the form:

f(x)=x^2+bx+c.

Then:

f(x^2+2)=(x^2+2)^2+b(x^2+2)+c = x^4+10x^2+4

Now expend the middle term and equate coefficients.

RonL