Final answer:
f(-1) for the function f(x) = 3^(2x) - 8 is calculated by substituting -1 into the equation, resulting in 3^(-2) - 8, which equals -7.8889 when rounded to the nearest ten-thousandth.
Step-by-step explanation:
To find the value of f(-1) for the function f(x) = 32x - 8, we need to substitute x with -1. First, calculate the exponent: 32(-1) = 3-2. To get 3-2, you need to take the reciprocal of 32, which is 1/32 or 1/9. In decimal form, 1/9 is approximately 0.1111. Now, subtract 8 from this value: 0.1111 - 8 = -7.8889. When expressed to the nearest ten-thousandth, the answer is -7.8889.