Thanks a bunch!
$\displaystyle f(x)$ 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 ...
$\displaystyle 4a = 1$ ... $\displaystyle a = \frac{1}{4}$
$\displaystyle 2b - 3 = 1$ ... $\displaystyle b = 2$
$\displaystyle \frac{9}{4} - 6 + c = -1$ ... $\displaystyle c = \frac{11}{4}$
$\displaystyle f(x) = \frac{x^2}{4} + 2x + \frac{11}{4}$