sandy wrote:
For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?
(A) \(f(x) = x^2\)
(B) \(f(x) = 5x\)
(C) \(f(x) = 2x + 1\)
(D) \(f(x) =\sqrt{x}\)
(E) \(f(x) = x - 2\)
One approach is to let a = 1 and b = 1 and plug in the values.
So, the question becomes, "Which of the following functions are such that f(1 + 1) = f(1) + f(1)?"
In other words,
for which function does f(2) = f(1) + f(1)?A) If f(x) = x², does f(
2) = f(
1) + f(
1)?
Plug in to get:
2² =
1² +
1²
No, doesn't work
So, it is
not the case that f(
2) = f(
1) + f(
1), when f(x) = x²
ELIMINATE A
B) If f(x) = 5x, does f(
2) = f(
1) + f(
1)?
Plug in to get: 5(
2) = 5(
1) + 5(
1)
It works. KEEP B for now.
C) If f(x) = 2x + 1, does f(
2) = f(
1) + f(
1)?
Plug in to get: 2(
2) + 1 = 2(
1) + 1 + 2(
1) + 1
No, doesn't work
So, it is
not the case that f(
2) = f(
1) + f(
1), when f(x) = 2x + 1
ELIMINATE C
D) If f(x) = √x, does f(
2) = f(
1) + f(
1)?
Plug in to get: √
2 = √
1 + √
1 No, doesn't work
So, it is
not the case that f(
2) = f(
1) + f(
1), when f(x) = √x
ELIMINATE D
E) If f(x) = x - 2, does f(
2) = f(
1) + f(
1)?
Plug in to get:
2 - 2 = (
1 - 2) + (
1 - 2)
No, doesn't work
So, it is
not the case that f(
2) = f(
1) + f(
1), when f(x) = x - 2
ELIMINATE E
By the process of elimination, the correct answer is B
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.comSign up for GRE Question of the Day emails