<s>[INST] If $f(3x-1)=9x^2+6x-7$, determine $f(x)$ if $f(3x-1)=9x^2+6x-7$ determine all the $f(x)$ functions. 
I tried in this way :
$t=3x-1 \Rightarrow x=(t+1)/3$
$f(t)=9(t+1)^2/9-6((t+1)/3)-7((t+1)/3)\ldots$
but unfortunately I get the original function.
Thanks in advance.
 [/INST] Using your method, substituting $t = 3x - 1 \iff x = \dfrac {t+1}{3} $, we have $$\begin{align} f(t) & = \dfrac{9(t+1)^2}{9} + \dfrac{6(t+1)}{3} - 7 \\ \\ & = (t+1)^2  +2(t+1) - 7 \\ \\ &= t^2 + 4t - 4 \end{align}$$
Hence, $$f(x) = x^2 + 4x - 4$$
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