Final answer:
To solve ((f)/(g))(8), we substitute x with 8 in both f(x) and g(x), finding their respective values and then dividing f(8) by g(8). The result is approximately 0.00002456.
Step-by-step explanation:
The question involves finding the value of the function ((f)/(g))(x) at x=8. The function f(x) is given as x3 - 2x2 + 4x - 4, and the function g(x) is 23x. We need to evaluate both functions at x=8 and then divide the result of f(8) by the result of g(8).
To find f(8), we substitute x with 8:
f(8) = 83 - 2(8)2 + 4(8) - 4
f(8) = 512 - 2(64) + 32 - 4
f(8) = 512 - 128 + 32 - 4
f(8) = 412
Now, we find g(8):
g(8) = 23(8)
g(8) = 224
g(8) = 16777216
Finally, we compute ((f)/(g))(8):
((f)/(g))(8) = f(8) / g(8)
((f)/(g))(8) = 412 / 16777216
((f)/(g))(8) ≈ 0.00002456