Final answer:
To find the value of 1/2g(-6)+f(-2), evaluate g(-6) and f(-2) and substitute the values into the expression.
Step-by-step explanation:
To find the value of 1/2g(-6)+f(-2), we first need to evaluate the functions g(x) and f(x) at the given values.
g(-6) = 14 - 2/3(-6) = 14 + 4 = 18
f(-2) = -(-2)^2 + 8(-2) - 11 = -4 - 16 - 11 = -31
Now, substitute the values of g(-6) and f(-2) into the expression 1/2g(-6)+f(-2):
1/2(18) + (-31) = 9 - 31 = -22