Final answer:
To calculate the function values (f + g)(-1) and (g - f)(-1), substitute x = -1 into f(x) and g(x), respectively, then perform the addition and subtraction to find that (f + g)(-1) = 12 and (g - f)(-1) = 38.
Step-by-step explanation:
The student has asked to calculate the function values for (f + g)(-1) and (g - f)(-1) where f(x) = 4x² + 7x - 10 and g(x) = -4x + 21. To find these values, we substitute x = -1 into each function and then perform the indicated operations.
First, we evaluate f(-1) and g(-1):
- f(-1) = 4(-1)² + 7(-1) - 10 = 4 - 7 - 10 = -13
- g(-1) = -4(-1) + 21 = 4 + 21 = 25
Now we can find (f + g)(-1) by adding f(-1) and g(-1):
(f + g)(-1) = f(-1) + g(-1) = -13 + 25 = 12
Similarly, to find (g - f)(-1), we subtract f(-1) from g(-1):
(g - f)(-1) = g(-1) - f(-1) = 25 - (-13) = 25 + 13 = 38