csat-suneung 2016 Q27

csat-suneung · South-Korea · csat__math-A 4 marks Curve Sketching Finding Parameters for Continuity
Two functions $$f ( x ) = \left\{ \begin{array} { l l } x + 3 & ( x \leq a ) \\ x ^ { 2 } - x & ( x > a ) \end{array} , \quad g ( x ) = x - ( 2 a + 7 ) \right.$$ Find the product of all real values of $a$ such that the function $f ( x ) g ( x )$ is continuous on the entire set of real numbers. [4 points]
Two functions
$$f ( x ) = \left\{ \begin{array} { l l } x + 3 & ( x \leq a ) \\ x ^ { 2 } - x & ( x > a ) \end{array} , \quad g ( x ) = x - ( 2 a + 7 ) \right.$$
Find the product of all real values of $a$ such that the function $f ( x ) g ( x )$ is continuous on the entire set of real numbers. [4 points]