Let f(x) = -2x + 4 and g(x) = -6x - 7.
a) Find f(x) * g(x).
b) Find f(g(4)).
a) To find f(x) * g(x), we need to multiply the two functions together:
f(x) * g(x) = (-2x + 4) * (-6x - 7)
Using the distributive property, we can expand this expression:
f(x) * g(x) = (-2x * -6x) + (-2x * -7) + (4 * -6x) + (4 * -7)
Simplifying each term, we get:
f(x) * g(x) = 12x^2 + 14x - 24x - 28
Combining like terms, we get the final answer:
f(x) * g(x) = 12x^2 - 10x - 28
b) To find f(g(4)), we first need to find g(4):
g(4) = -6(4) - 7
g(4) = -31
Now we can substitute this value into f(x):
f(g(4)) = f(-31)
f(-31) = (-2(-31) + 4)
f(-31) = 66
Therefore, f(g(4)) = 66.