Funtion problem

[geetesht]

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?
a) f(x)=x^2
b) f(x)=x+1
c) f(x)= sq root of x
d) f(x)=2/3
e) f(x)=-3x

OA (E)

Anyone could you please help!

[tigerwoods]

hi you made a transcribing error in choice D..........

This is the actual question, its been discussed before already...... try to do a search you will find a lot questions already discussed here.......


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
D) f(x) = 2/x
E) f(x) = -3x


Because this is a problem solving question, and the stem states, "for all positive numbers a and b," I would just pick numbers. a=1 b=3

A. f(1+3) = f(1)+f(3)
4^2 = 1^2 + 3^2
16=2+9 => NO
B. (4+1) = (1+1) + (3+1)
5=2+4 => NO
C. √4 = √1 + √3
2=1+√3 => NO
D. 2/4 = 2/1 + 2/3
1/2 = 8/3 => NO
E. -3(4) = -3(1) + -3(3)
-12 = -12 => YES

[Ben Ku]

Here's a link to a solution for this problem.
http://www.manhattangmat.com/forums/for-which-of-the-following-functions-is-f-a-b-f-a-f-b-t2795.html

Hope it helps.