Final answer:
To determine f(-2) for the given piecewise function, we use the second part of the function which is 2x²-9 since -2 falls within the domain -3≤x<4, resulting in f(-2) = -1.
Step-by-step explanation:
The question involves evaluating a piecewise function at a particular value, specifically f(-2). To understand which part of the piecewise function to use, we must look at the domain conditions given for each segment of the function.
The function is defined in three parts:
- For x<-3, the function is x³.
- For -3≤x<4, it is 2x²-9.
- For x≥4, the function is 5x+4.
Since -2 is within the domain -3≤x<4, we use the second part of the function to evaluate f(-2), which yields f(-2)=2(-2)²-9=2(4)-9=8-9=-1.