Roots of Transformed Functions

Suppose an equation  
  has solutions  
\[x=-3, \; 1, \; 2\]
The function is then transformed to become  
. What will be the solutions of the equation  
The function actually tells us that  
. We should be solving
\[f(3x-2)=f(-3) \rightarrow 3x-2=-3 \rightarrow 3x=2-3=-1 \rightarrow x =- \frac{1}{3}\]

\[f(3x-2)=f(1) \rightarrow 3x-2=1 \rightarrow 3x=2+1=3 \rightarrow x =1\]

\[f(3x-2)=f(2) \rightarrow 3x-2=2 \rightarrow 3x=2+4=4 \rightarrow x = \frac{4}{3}\]

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