Question: The functions \( f(x) = x^2 - 3x + k \) and \( g(x) = x^2 - 3x + 2k \) are evaluated when \( x = 3 \). What is the value of \( k \) if \( f(3) = g(3) \)?

["Question: The functions ( f(x) = x^2 - 3x + k ) and ( g(x) = x^2 - 3x + 2k ) are evaluated when ( x = 3 ). What is the value of ( k ) if ( f(3) = g(3) )?", "---", "Answer:\nWhen evaluating functions at ( x = 3 ), we substitute ( x = 3 ) into each expression and set them equal since ( f(3) = g(3) ).", "Given:\n[\nf(x) = x^2 - 3x + k \quad \Rightarrow \quad f(3) = 3^2 - 3(3) + k = 9 - 9 + k = k\n]", "[\ng(x) = x^2 - 3x + 2k \quad \Rightarrow \quad g(3) = 3^2 - 3(3) + 2k = 9 - 9 + 2k = 2k\n]", "Set the two expressions equal:\n[\nf(3) = g(3) \Rightarrow k = 2k\n]", "Subtract ( k ) from both sides:\n[\n0 = k\n]", "Thus, the value of ( k ) is ( 0 ).", "---", "Understanding when two quadratic functions yield the same output at a specific input value helps build foundational skills in function analysis, which is essential in algebra and advanced mathematics. For function identification problems like this, setting equations equal at given ( x ) values simplifies solving for unknown parameters efficiently.", "Keywords: ( f(x) = x^2 - 3x + k ), ( g(x) = x^2 - 3x + 2k ), ( f(3) = g(3) ), value of ( k ), solving for ( k ), algebra problem solution, function equality at ( x = 3 ), math problem step-by-step."]