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.