SOLUTION: Please help me solve this problem. Thank you. If f(2x-1) = 8x^3 - 12x^2 + 4x what is f(x)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this problem. Thank you. If f(2x-1) = 8x^3 - 12x^2 + 4x what is f(x)?      Log On


   

Question 996952: Please help me solve this problem. Thank you. If f(2x-1) = 8x^3 - 12x^2 + 4x what is f(x)?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You want an input of x instead of input of 2x-1. Maybe the inverse of 2x-1 will be that input x.

L%28x%29=2x-1
L%5E-1%28x%29 should be inverse of L.
2%2AL%5E%28-1%29-1=x
2%2AL%5E%28-1%29=x%2B1
L%5E%28-1%29=%28x%2B1%29%2F2

You want to form f%28L%28L%5E%28-1%29%28x%29%29%29
-
This should be f(x): 8%28%28x%2B1%29%2F2%29%5E3+-+12%28%28x%2B1%29%2F2%29%5E2+%2B+4%28x%2B1%29%2F2

%28x%2B1%29%5E3-3%28x%2B1%29%5E2%2B2%28x%2B1%29
which is still much in unsimplified form.
You can do what you need or want with it, but that should be equivalent to f(x).