Function Question

[Atonio79]

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)= x^(1/2)
d. f(x)= 2/x
e. f(x)= -3x

[Retake_GMAT]

f(x) = x^2

f(a + b) = (a+b)^2 which is not equal to a^2 + b^2 i.e. f(a) + f(b)


f(x) = x + 1

f(a + b) = a+b+1 which is not equal to a+1 + b+1 i.e. f(a) + f(b)


f(x) = sqrt x

f(a + b) = sqrt(a+b) which is not equal to sqrt(a) + sqrt(b) i.e. f(a) + f(b)


f(x) = 2/x

f(a + b) = 2/(a+b) which is not equal to 2/a + 2/b i.e. f(a) + f(b)


f(x) = -3 x

f(a + b) = -3(a+b) = -3a -3b = f(a) + f(b)

ans E

[Anson800]

Imo E

[GmatG]

Originally Posted by Retake_GMAT

f(x) = x^2

f(a + b) = (a+b)^2 which is not equal to a^2 + b^2 i.e. f(a) + f(b)


f(x) = x + 1

f(a + b) = a+b+1 which is not equal to a+1 + b+1 i.e. f(a) + f(b)


f(x) = sqrt x

f(a + b) = sqrt(a+b) which is not equal to sqrt(a) + sqrt(b) i.e. f(a) + f(b)


f(x) = 2/x

f(a + b) = 2/(a+b) which is not equal to 2/a + 2/b i.e. f(a) + f(b)


f(x) = -3 x

f(a + b) = -3(a+b) = -3a -3b = f(a) + f(b)

ans E

IMO E. Same as above.

[NishantG]

E for me too

f(a+b) = f(a) + f(b)

if f(a) = -3a

f(a+b) = -3(a+b) = -3a -3b = f(a) + f(b)

[Atonio79]

The Correct Answer is E... Thanks for explanation!