For which of the following does f(x)−f(y)=f(x−y) for all values of x and y?  Choices:
A) f(a)=a^2
B) f(a)=a/2
C) f(a)=a+5
D) f(a)=2a−1
E) f(a)=|a|
To solve this easiest way is just put the value and see that if it equals or not.   with option 1. f(x) = x^2 and f(y) = y^2   so L.H.S = x^2 - y^2   and R.H.S = (x-y)^2 ==&gt; x^2 + y^2 -2xy.   so L.H.S not equal to R.H.S   with option 2. f(x) = x/2 and f(y) = y/2   L.H.S = x/2 - y/2 ==&gt; 1/2(x-y)   R.H.S = (x-y)/2   so L.H.S = R.H.S which is the correct answer.   f(a)=a/2
<result>B</result>
For which of the following does f(x)−f(y)=f(x−y) for all values of x and y?