a. To find f(-4), we simply substitute -4 for x in the function f(x):
f(-4) = (-4)² - 3(-4) = 16 + 12 = 28
Therefore, f(-4) = 28.
b. To find g(1)-f(-3), we first need to find g(1) and f(-3) separately.
g(1) = 2(1) - 5 = -3
f(-3) = (-3)² - 3(-3) = 9 + 9 = 18
Then, we can substitute these values into the expression:
g(1)-f(-3) = -3 - 18 = -21
Therefore, g(1)-f(-3) = -21.
c. To find f(g(-4)), we first need to find g(-4) and then substitute this value into f(x).
g(-4) = 2(-4) - 5 = -8 - 5 = -13
Then, we can substitute -13 for x in the function f(x):
f(g(-4)) = (-13)² - 3(-13) = 169 + 39 = 208
Therefore, f(g(-4)) = 208.