Answer:
-1/2
Explanation:
To find p^6(-1/2), we need to repeatedly apply the function p(x) to the value -1/2 six times:
p(x) = 1 - 1/x
p(-1/2) = 1 - 1/(-1/2) = 1 - (-2) = 3
p(p(-1/2)) = p(3) = 1 - 1/3 = 2/3
p(p(p(-1/2))) = p(2/3) = 1 - 3/2 = -1/2
p(p(p(p(-1/2)))) = p(-1/2) = 3
p(p(p(p(p(-1/2))))) = p(3) = 1 - 1/3 = 2/3
p(p(p(p(p(p(-1/2)))))) = p(2/3) = 1 - 3/2 = -1/2
Therefore, p^6(-1/2) = -1/2.