:confused::confused:

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!!!!!!:)

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- Oct 13th 2007, 09:41 AMrlarachPolynomial Funtion HELP PLEASE!!!
:confused::confused:

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!!!!!!:) - Oct 13th 2007, 09:50 AMtopsquark
Well, the "brute force" method would be:

$\displaystyle f(x^2 + 2) = x^4 + 10x^2 + 4$

Let $\displaystyle y = x^2 + 2$.

Solve for x:

$\displaystyle x^2 = y - 2$

$\displaystyle x = \pm \sqrt{y - 2}$

Ignoring the difficulty of the $\displaystyle \pm$ let's blithely continue:

$\displaystyle f(y) = ( \pm \sqrt{y - 2} )^4 + 10 ( \pm \sqrt{y - 2} ) + 4$

$\displaystyle f(y) = (y - 2)^2 + 10(y - 2) + 4$

Now let $\displaystyle y = x^2 - 2$.

$\displaystyle f(x^2 - 2) = (x^2 - 2 - 2)^2 + 10(x^2 - 2 - 2) + 4$

$\displaystyle f(x^2 - 2) = (x^2 - 4)^2 + 10(x^2 - 4) + 4$

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

-Dan - Oct 13th 2007, 09:57 AMCaptainBlack
- Oct 13th 2007, 11:16 AMrlarach
How Do You Get X^2 + 6x - 12

- Oct 13th 2007, 01:11 PMCaptainBlack