IMO - e
f(x)=-3x
so, f(a+b) = -3(a+b)=-3a-3b
f(a)+f(b)= -3a+(-3b)=-3a-3b
problem with functions Gmat Prep
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Source: Beat The GMAT — Problem Solving |
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Taniuca wrote:For wich 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) = SQRx
d)f(x)= 2/x
e)f(x)=-3x
Let's analyze each of the options individually:
1. (a + b)² ≠(a² + b²) => f(a + b) ≠f(a) + f(b)
2. (a + b + 1) ≠(a + 1) + (b + 1) = (a + b + 2) => f(a + b) ≠f(a) + f(b)
3. √(a + b) ≠(√a + √b) => f(a + b) ≠f(a) + f(b)
4. 2/(a + b) ≠(2/a) + (2/b) = 2(a + b)/ab => f(a + b) ≠f(a) + f(b)
5. (-3(a + b)) = (-3a) + (-3b) => f(a + b) = f(a) + f(b)
The correct answer is E.
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