Thanks a bunch!

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#### skeeter

MHF Helper
$$\displaystyle f(x)$$ is quadratic ...

$$\displaystyle f(x) = ax^2 + bx + c$$

$$\displaystyle f(2x-3) = a(2x-3)^2 + b(2x-3) + c = x^2 + x - 1$$

$$\displaystyle f(2x-3) = a(4x^2-12x+9) + b(2x-3) + c = x^2 + x - 1$$

$$\displaystyle 4ax^2 + (2b-12a)x + (9a-3b+c) = x^2 + x - 1$$

equate coefficients ...

$$\displaystyle 4a = 1$$ ... $$\displaystyle a = \frac{1}{4}$$

$$\displaystyle 2b - 3 = 1$$ ... $$\displaystyle b = 2$$

$$\displaystyle \frac{9}{4} - 6 + c = -1$$ ... $$\displaystyle c = \frac{11}{4}$$

$$\displaystyle f(x) = \frac{x^2}{4} + 2x + \frac{11}{4}$$