Final answer:
The expression for (s + t)(x) is 3x + 11 by adding the two functions, and the value of (s · t)(-2) is 6, which is the result of multiplying the functions' values at x = -2. The notation (s, t)(x) is not used correctly in this context, and none of the provided answers are correct.
Step-by-step explanation:
Given the functions s(x) = x + 5 and t(x) = 2x + 6, we want to find the expressions for (s, t)(x), (s + t)(x), and evaluate (s · t)(-2).
The notation (s, t)(x) is unclear, as it is not standard notation for operations on functions. It is possible that it represents either the ordered pair (s(x), t(x)) or a composition of the functions s(t(x)) or t(s(x)). However, the provided answers do not seem to align with these interpretations, so let's instead focus on the operations explicitly mentioned: addition and multiplication of the functions.
To find (s + t)(x), we add s(x) to t(x):
(s + t)(x) = s(x) + t(x) = (x + 5) + (2x + 6) = 3x + 11.
To evaluate (s · t)(-2), we multiply s(-2) by t(-2):
(s · t)(-2) = s(-2) · t(-2) = 3 · 2 = 6.
Therefore, (s + t)(x) = 3x + 11, and (s · t)(-2) = 6. There seems to be an error or misunderstanding regarding what (s, t)(x) refers to, and the correct evaluation of (s · t)(-2). None of the provided answers (a, b, c, d) contain these correct results.