Vincen wrote: ↑Fri May 28, 2021 6:50 am
For which of the following functions is \(f(a + b) = f(a) + f(b)\) for all positive numbers \(a\) and \(b?\)
A. \(f(x)=x^2\)
B. \(f(x)=x+1\)
C. \(f(x)=\sqrt{x}\)
D. \(f(x)=\dfrac2{x}\)
E. \(f(x)=-3x\)
Answer:
E
Source: GMAT Prep
One approach is to
plug in numbers. Let's
let a = 1 and b = 1
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
B) If f(x)=x+1, does f(
2) = f(
1) + f(
1)?
Plug in to get:
2+1 =
1+1 +
1+1? (No, doesn't work)
So, it is
not the case that f(
2) = f(
1) + f(
1)
.
.
.
A, B, C and D do not work.
So, at this point, we can conclude that E must be the correct answer.
Let's check E anyway (for "fun")
E) If f(x)=-3x, does f(
2) = f(
1) + f(
1)?
Plugging in 2 and 1 we get: (-3)(
2) = (-3)(
1) + (-3)(
1)
Yes, it works
The correct answer is E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
