Final answer:
To evaluate the expressions (f g)(3), (f−g)(2), (f⋅g)(0), and (fg)(1), we substitute the given values into the functions and perform the operations. The results are 2, 16, 100, and 112 respectively.
Step-by-step explanation:
To evaluate the given expressions, we substitute the given values into the functions.
For (f g)(3), we first evaluate g(3) which gives us 3 - 5 = -2. Then we substitute this value into f(x) which gives us f(-2) = (-2)² - 9(-2) - 20 = 4 + 18 - 20 = 2.
Similarly, for (f−g)(2), we first find g(2) which gives us 2 - 5 = -3. Then we substitute this value into f(x) which gives us f(-3) = (-3)² - 9(-3) - 20 = 9 + 27 - 20 = 16.
For (f⋅g)(0), we find f(0) = 0² - 9(0) - 20 = -20 and g(0) = 0 - 5 = -5. Multiplying these values gives us (-20) * (-5) = 100.
Finally, for (fg)(1), we find f(1) = 1² - 9(1) - 20 = 1 - 9 - 20 = -28 and g(1) = 1 - 5 = -4. Multiplying these values gives us (-28) * (-4) = 112.