Question

If f(x) = 3^{2x}-8, what is the value of )f(−1), to the nearest ten-thousandth (if necessary)?

Answer 1

The value of f(-1) for the function f(x) = 3^(2x) - 8 is found by evaluating 3^(-2) and subtracting 8, which results in -71/9 or approximately -7.8889 to the nearest ten-thousandth.

Step-by-step explanation:

To find the value of f(-1) for the function f(x) = 32x - 8, we substitute -1 for x and follow the steps to solve:

1. Calculate the exponent: 2(-1) = -2.
2. Compute the base raised to the computed exponent: 3-2.
3. To evaluate 3-2 without a calculator, remember that a negative exponent implies the reciprocal. Thus, 3-2 = 1/32 = 1/9.
4. Finally, subtract 8 from this result: 1/9 - 8.
5. To avoid negative fractions, convert -8 to ⅘/9 which is equal to -72/9. Now you have (1 - 72)/9 = -71/9.

Therefore, f(-1) is equal to -71/9, to the nearest ten-thousandth, f(-1) is -7.8889.