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Given f(x)=x^(3)-2ˣ²+4x-4 and g(x)=2³ˣ, find ((f)/(g))(8) Your answer may be exact or rounded to two decimal places.

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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

User Martin De Simone
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