APFIVE Valid Solutions for a Piecewise Function
For the piecewise function f defined by $$ f(x) = \begin{cases} 2x+1 & \text{if } x < 3 \\ x^2-4x+3 & \text{if } x \ge 3 \end{cases} $$, find the complete set of valid solutions for x by solving 2x+1 = 7 and x^2-4x+3 = 0 within their respective domains.
A
The solutions are $$x = 1$$ and $$x = 3$$.
B
The only solution is $$x = 3$$.
C
There are no solutions.
D
The only solution is $$x = 1$$.
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