3 Tips for Confusing Function Questions:
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 = . 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) =
C) f(x) =
D) f(x) =
E) f(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:
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?
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!