3 Tips for Confusing Function Questions:

by on June 14th, 2011

Function questions can be some of the most confusing math questions appearing on the GMAT.  Remember these 3 tips to attack these often complicated questions.

1. Look for the new definition.

In symbol functions, the test makers choose a new symbol, something that you probably haven’t seen before, and give it a new definition. You aren’t supposed to already know the meaning of the new symbol in the same way you know common math symbols like +, -, x and ÷. The question will tell you exactly how the new symbol functions.

Let z € y be defined by the equation z € y = z^2 - 1/y. What is the value of 3 € 1?

Here we plug in 3 for z and 1 for y to solve.


9 – 1


2. Replace abstracts with numbers.

For questions with functions in the answer choices, use the given definitions to substitute in for x.

For which of the following functions f is f(x) = f(1 – x) for all x?

A) f(x) = 1 – x
B) f(x) = 1-x^2
C) f(x) = x^2-(1-x)^2
D) f(x) = {x^2 }(1-x)^2
E) f(x) = x / 1-x

For instance, since  f(x) = f(1-x), one can easily and quickly notice that f(4)=f(-3).

If you notice that, then it is very easy to find the solution. Replace each function with 4 and -3 instead of x, and see if f(4)=f(-3).

A: F(-3) = 1 – (-3) = 4

F(4) = 1  – (4) = -3

They are NOT equal. Eliminate. Continue this method with the other choices, until you find the function for which the value you get when you plug in 4 is the same as when you plug in –3. That choice is D:

D:  F(-3) = (-3)^2 *(1-(-3))^2 = (9)(16)
F(4) = (4)^2 *(1-(4))^2 = (16)(9)
F(-3) = F(4).

So D is the correct answer.

3. Use the answer choices.

Let the function $x be defined as $x = (x + 3)(x – 3).

If $a = a + 3, what is one possible value for a?

A  9
B  6
C  4
D  3
E  0

Plug in the answer choices into the function to see which one will yield a + 3. Since the answer choices are listed numerically, let’s start with answer choice C. If our answer is too large, we will be able to eliminate A and B as well. If it’s too small, we’ll eliminate D and E.

C : $4 = (4 + 3)(4 – 3)
$4 = (7)(1) = 7

7 does equal 4 + 3, so C must be the correct answer!


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