If $f(x)=\frac{3x-2}{5x+3}$ where $f:\mathbb{R}-\{-\frac{3}{5}\}\rightarrow\mathbb{R}$ is defined, then $f\circ f(1)$ is
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Logic Tip: Alternatively, finding the composite function $f(f(x))$ first yields $\frac{3(\frac{3x-2}{5x+3})-2}{5(\frac{3x-2}{5x+3})+3} = \frac{-x-12}{30x-1}$. Substituting $x=1$ directly gives $\frac{-1-12}{30-1} = \frac{-13}{29}$. Both methods are robust, but sequential numerical substitution usually poses fewer chances for algebraic sign errors.