Answer:
- 21
- -42
Step-by-step explanation:
You want the values of different compositions of the functions f(x) and g(x) for different values of x.
1. Limit
The meaning of ...
[tex]\displaystyle\lim_{x\to-3^-}(\ )[/tex]
is that you want the limit of the expression as x approaches -3 from the left. In this problem, the functions are defined differently for values of x less than -3 than for values of x greater than -3.
You want to use the function definition that applies for x < -3. In each case, it isn't clear whether the function is actually defined at x = -3, but that doesn't matter for the purpose here. The limiting values of the functions are the values the function approaches as x approaches -3.
For f(x), the graph approaches 0 from the left at x=-3.
For g(x), the graph approaches -3 from the left at x=-3.
Then the composition is ...
f(x) -7g(x) = 0 -7(-3) = 21
2. Evaluation
For this problem, you need to know the values of f(-8) and g(-8). These are found in the usual way: read the graph. Locate -8 on the x-axis and follow the vertical line to the function curve. The function value is the y-coordinate of that point.
f(-8) = 6
g(-8) = 3
The value of the composition for x=-8 is ...
x·f(x) +2·g(x) = (-8)(6) +2(3) = -48 +6 = -42
