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.

There are no solutions.

The only solution is $x = 3$ .

The solutions are $x = 1$ and $x = 3$ .

The only solution is $x = 1$ .

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