1. **State the problem:** Simplify the expression $f(2x-1)$ given the function $f(x) = -2 + 3x$. 2. **Recall the function definition:** The function is defined as $f(x) = -2 + 3x$. 3. **Substitute the input:** Replace $x$ in the function with $2x - 1$ to find $f(2x-1)$. 4. **Write the substitution:** $$f(2x-1) = -2 + 3(2x - 1)$$ 5. **Distribute the 3:** $$f(2x-1) = -2 + 3 \times 2x - 3 \times 1 = -2 + 6x - 3$$ 6. **Combine like terms:** $$f(2x-1) = ( -2 - 3 ) + 6x = -5 + 6x$$ 7. **Final simplified expression:** $$\boxed{f(2x-1) = 6x - 5}$$ This means when you input $2x-1$ into the function $f$, the output simplifies to $6x - 5$.