Using f(x) = x(4-x) write the equations of

a) f(-2x)
b+ -f([1/2]x)

To find the equations of the given functions, we need to substitute the given values into the original function, f(x) = x(4 - x), and simplify.

a) For f(-2x):

1. Substitute -2x for x in f(x): f(-2x) = (-2x)(4 - (-2x)).

2. Simplify the expression inside the parentheses: f(-2x) = (-2x)(4 + 2x) = -2x(4 + 2x).

b) For -f([1/2]x):

1. Substitute [1/2]x for x in f(x): f([1/2]x) = [1/2]x(4 - [1/2]x).

2. Simplify the expression inside the parentheses: f([1/2]x) = [1/2]x(4 - x/2) = [1/2]x(8/2 - x/2) = [1/2]x(8 - x)/2 = [1/2]x(8 - x)/2.

Therefore, the equations are:
a) f(-2x) = -2x(4 + 2x).
b) -f([1/2]x) = [1/2]x(8 - x)/2.