f(x) = |4 -2x| has an absolute minimum of
A) 4
B) 2
C) -4
D) -8
E) 0

Question

Quizplus · Accepted Answer

Since f(x) is defined as the absolute value of an expression, the minimum value of f(x) is 0 when the expression is equal to 0. 
Setting the expression equal to 0:
|4 F1F1F1S1F1F1F10 2x| = 0
4 F1F1F1S1F1F1F10 2x = 0
Solving for x:
x = (F1F1F1S1F1F1F10)/4
Substituting this value of x into the original equation yields:
f(x) = |4 F1F1F1S1F1F1F10 2((F1F1F1S1F1F1F10)/4)|
f(x) = |2(F1F1F1S1F1F1F10)|
f(x) = 2|F1F1F1S1F1F1F10|
Since absolute value is always non-negative, the minimum value of f(x) is 0. Therefore, the answer is E: 0.

F(x) = |4 -2x| Has an Absolute Minimum of