Bunuel wrote:

For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?

(A) \(f(x) = x^2\)

(B) \(f(x) = 5x\)

(C) \(f(x) = 2x + 1\)

(D) \(f(x) =\sqrt{x}\)

(E) \(f(x) = x - 2\)

Instead of trying to work with the equations, we'll pick easy numbers to eliminate incorrect answers.

This is an Alternative approach.

Say a = 1 and b = 1, so a+b = 2.

Then (A) gives f(2) = 4 but f(1) + f(1) = 2. NO!

(B) gives f(2) = 10 and f(1)+f(1) = 10. Maybe let's check the others.

(C) gives f(2) = 5 but f(1) + f(1) = 6. NO!

(D) gives f(2) = \(\sqrt{2}\) while f(1)+f(1) = 2. NO

(E) gives f(2) = 0 and f(1) + f(1) = -2. NO

(B) must be our answer.

In my opinion, it is very basic fundamental question. I don't know whether we really need number to put in and check. If student's basic math fundamentals are clear, Student should be able to solve it visually.