PS3

winter wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?

1) f(x) = x square
2) f(x) = x + 1
3) f(x) = underroot x
4) f(x) = 2/x
5) f(x) = -3x

Let's check each of the options one by one.
(1) f(a+b) = (a+b)^2 = a^2 + 2ab + b^2. But f(a) + f(b) = a^2 + b^2. So (1) is not true.
(2) f(a + b) = (a+b +1). But f(a) + f(b) = a+1 + b+1 = a+b+2. So (2) is not true.
(3) f(a+b) = √(a+b). But f(a) + f(b) = √a + √b. So (3) is not true.
(4) f(a+b) = 2/(a+b). But f(a) + f(b) = 2/a + 2/b = 2(a+b)/ab. So (4) is not true.
(5) f(a+b) = -3(a+b). But f(a) + f(b) = -3a - 3b = -3(a +b) = f(a+b). Hence, (5) is true.

The correct answer is (5).

sumanr84 wrote: These are generally added in the test as Time Busters as we need to check for all options. Start either from Middle or Last. I prefer from Last.

You are correct!