Let a=2 and b=3.For which of the following does f(a)-f(b)=f(a-b) for all values of a and b?
A) f(x)=x²
B) f(x)=x/2
C) f(x)=x+5
D) f(x)=2x−1
E) f(x)=|x|
Then:
f(a) = f(2).
f(b) = f(3).
f(a-b) = f(2-3) = f(-1).
The question stem becomes:
For which of the following does f(2) - f(3) = f(-1)?
A) f(x)=x²
f(2) = 2² = 4.
f(3) = 3² = 9.
f(-1) = (-1)² = 1.
Substituting these values into f(2) - f(3) = f(-1), we get:
4-9 = 1
-5 = 1.
Doesn't work.
Eliminate A.
B) f(x)=x/2
f(2) = 2/2.
f(3) = 3/2.
f(-1) = -1/2.
Substituting these values into f(2) - f(3) = f(-1), we get:
2/2 - 3/2 = -1/2
-1/2 = -1/2.
This works.
Hold onto B.
C) f(x)=x+5
f(2) = 2+5 = 7.
f(3) = 3+5 = 8.
f(-1) = -1+5 = 4.
Substituting these values into f(2) - f(3) = f(-1), we get:
7+8 = 4
15 = 4.
Doesn't work.
Eliminate C.
D) f(x)=2x−1
f(2) = 2*2 - 1 = 3.
f(3) = 2*3 - 1 = 5.
f(-1) = 2(-1) - 1 = -3.
Substituting these values into f(2) - f(3) = f(-1), we get:
3-5 = -3
-2 = -3.
Doesn't work.
Eliminate D.
E) f(x)=|x|
f(2) = |2| = 2.
f(3) = |3| = 3.
f(-1) = |-1| = 1.
Substituting these values into f(2) - f(3) = f(-1), we get:
2-3 = 1
-1 = 1.
Doesn't work.
Eliminate E.
The correct answer is B.
