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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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
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