Final answer:
The value of f(-3) for the given function when x ≤ -1 is 728.25. The function at this interval is f(x) = (x³)² - 3 - x - ¾, and upon evaluation, the value is determined.
Step-by-step explanation:
To find the value of f(-3) for the function given in the question, we need to look at the definition of the function in different intervals. Since x ≤ -1 for f(-3), we use the definition f(x) = (x³)² - 3 - x - ¾. We then substitute -3 for x in the function:
f(-3) = ((-3)³)² - 3 - (-3) - ¾
Now, we evaluate this expression:
f(-3) = (27)² - 3 + 3 - ¾
f(-3) = 729 - ¾
f(-3) = 728.25
So, the value of f(-3) is 728.25, which falls in the interval where x ≤ -1.