Hi, I'm happy to help with this.
This is a tricky question! It helps to know a good deal about functions to answer this questions, but that's a topic that is for the most part well beyond the realm of GMAT math. Furthermore, many of the answer choices play on very common mathematical mistakes.
To demonstrate the solution, I'll just plug each function into the expression
A) f(x) = x^2
f(a + b) = (a + b)^2 = a^2 + 2ab + b^2
f(a) + f(b) = a^2 + b^2
not equal
BTW, it's a very tempting algebra mistake to think that (a + b)^2 is the same as a^2 + b^2.
B) f(x) = x + 1
f(a + b) = (a + b)^2 = a + b + 1
f(a) + f(b) = (a + 1) + (b + 1) = a + b + 2
not equal
C) f(x) = √x
f(a + b) = √(a + b)
f(a) + f(b) = √(a) + √(b)
not equal
Again, another very tempting algebra mistake. Folks are always tempted to say that √(a + b) is the same as √(a) + √(b). It doesn't work --- for example, if a = 9, and b = 16, then √(a + b) = √25 = 5, but √(a) + √(b) = √9 + √16 = 3 + 4 = 7
D) f(x) = 2/x
f(a + b) = 2/(a + b)
f(a) + f(b) = 2/(a) + 2/(b)
not equal
Yet another very tempting algebra mistake. Folks often want to equal 1/(a + b) with (1/a) + (1/b), but you can't combine or separate fractions by addition/subtraction unless then have a common denominator.
E) f(x) = -3x
f(a + b) = -3*(a + b) = -3a -3b
f(a) + f(b) = -3*(a) + -3*(b) = -3a -3b
these are equal!
Answer =
E
Does all this make sense? There's a lot of important math here. Please let me know if you have any questions on what I've written.
Mike
