Answer:
the values of A, B, and C are A = 0, B = -4, and C = 0.
Explanation:
To find f(1-x), we can substitute (1-x) for x in the expression for f(x):
f(1-x) = -2^(-3(1-x)) = -2^(-3+3x)
We can simplify this expression as follows:
f(1-x) = -2^(-3+3x) = -2^3 * 2^(3x) = -8 * (2^x)^3
Now we can substitute (1-x) for x in the expression for f(x), and use the simplified expression above to write f(1-x) as a polynomial in x:
f(1-x) = -8 * (2^x)^3 = -8 * (2^(1-x))^3 = -8 * (1/2^x)^3
= -8 * (1/2)^(3(1-x)) = -8 * (1/8) * (1/2)^(-3x)
= -1/2^(-3x+1) = -2^(3x-1)
Thus, we can see that f(1-x) can be written in the form Ax^2 + Bx + C, where:
A = 0 (because there is no x^2 term in the expression for f(1-x))
B = -2^2 = -4 (because the coefficient of the x term is -2^(3-1) = -2^2 = -4)
C = 0 (because there is no constant term in the expression for f(1-x))
Therefore, the values of A, B, and C are A = 0, B = -4, and C = 0.