Final answer:
To find the value of h(f(g(-½))), the greatest integer function gives us -1 for g(-½), the signum function then yields -1 for f(-1), and the absolute value function gives us 1 for h(-1). So, the result is 1.
Step-by-step explanation:
To find the value of h(f(g(-½))), let's evaluate it step by step considering the functions involved, which are the signum function (f(x)), the greatest integer function (g(x)), and the absolute value function (h(x)).
Firstly, we evaluate g(-½), which is the greatest integer function. The greatest integer function of any number is the largest integer that is less than or equal to the number. Hence, g(-½) is -1 since -1 is the largest integer that is not greater than -½.
Next, we find f(g(-½)), which means we apply the signum function to -1. The signum function of a negative number is -1. Therefore, f(-1) is -1.
Finally, we apply the absolute value function to f(g(-½)), which is h(f(-1)). The absolute value of -1 is 1, so h(-1) is 1. Hence, the final value of h(f(g(-½))) is 1.