If f(x) = x + 1/2x^2 - 1 and g(x) = 2f(2x), then g(1/2) = ?

First, we need to find the value of f(2x) by substituting 2x into the function f(x):

f(2x) = 2x + 1/2(2x)^2 - 1
f(2x) = 2x + 1/2(4x^2) - 1
f(2x) = 2x + 2x^2 - 1

Now, we can find g(x) by substituting f(2x) into the function g(x):

g(x) = 2(2x + 2x^2 - 1)
g(x) = 4x + 4x^2 - 2

Finally, we can find g(1/2) by substituting 1/2 into the function g(x):

g(1/2) = 4(1/2) + 4(1/2)^2 - 2
g(1/2) = 2 + 4(1/4) - 2
g(1/2) = 2 + 1 - 2
g(1/2) = 1

Therefore, g(1/2) = 1.

f(x) = x 1/2x^2 - 1
g(x) = 2f(2x) = 2(2x 1/2(2x)^2 - 1) = 2(2x 2x^2 - 1) = 2(2x^3 - x - 1) = 4x^3 - 2x - 2

g(1/2) = 4(1/2)^3 - 2(1/2) - 2 = 1/2 - 2 - 2 = -3.5