Final answer:
To evaluate the function q(p) at a specific value, we substitute the value into the appropriate part of the piecewise function. In this case, q((-1)/(2)) = 3/4.
Step-by-step explanation:
To evaluate the function q(p), we need to substitute the value of p into the appropriate part of the piecewise function. In this case, we are given q(p)=(-3p,p<=-1),(-3p²-3p,-1<=p<=1),(-3p³-3p²,p>1). We need to find q((-1)/(2)).
Since (-1)/(2) is greater than -1 and less than or equal to 1, we substitute it into the second part of the function. q((-1)/(2)) = -3((-1)/(2))²-3((-1)/(2)) = -3(1/4) - 3(-1/2) = -3/4 + 3/2 = -3/4 + 6/4 = 3/4.
Therefore, q((-1)/(2)) = 3/4.