What Is Functions on the GMAT?
Functions on the GMAT are all about rules that map inputs to outputs. They show up in two main forms: defined operations (like x△y) and classic function questions (like f(x)). Understanding how to interpret and manipulate these rules is key to solving a variety of quant problems efficiently.
Definition
A function is a rule that assigns each input exactly one output. On the GMAT, you’ll see functions in two ways:
- Defined operations: The test defines a new symbol (e.g., x△y = x² + y²) and asks you to compute with it.
- Standard function notation: You’ll see f(x) = ... and need to evaluate it for specific inputs, or compose functions.
In both cases, the key is to substitute the given numbers into the rule exactly as written.
Why It Matters on the GMAT
Function questions test your ability to follow rules precisely and spot patterns. They appear in both Problem Solving and Data Sufficiency, and they often combine with other topics like algebra, arithmetic, or number properties. Missing a small detail in the rule can lead to a wrong answer, so careful substitution is crucial. Also, function questions are a favorite for testing your understanding of order of operations and parentheses.
A Concrete Example
Suppose the GMAT defines x△y = x² − y². What is 5△3?
Substitute: 5² − 3² = 25 − 9 = 16. So 5△3 = 16.
Now consider a classic function: If f(x) = 2x + 1, find f(f(2)). First compute f(2) = 2(2) + 1 = 5, then f(5) = 2(5) + 1 = 11. So the answer is 11.
Common Mistakes
- Misreading the rule: Forgetting to apply the operation to both parts, or mixing up the order (e.g., using y² − x² instead of x² − y²).
- Ignoring parentheses: In defined operations, the symbol often includes parentheses; treat them as grouping symbols.
- Forgetting to substitute correctly: When given a function like f(x + 1), you must replace every x in the rule with (x + 1), not just the first one.
- Not simplifying fully: Sometimes the answer choices are simplified forms; always reduce your result.
How to Practice It
Start by drilling defined operations with simple symbols. Write out the substitution step explicitly. Then move to nested functions and compositions, like f(g(x)). Use official GMAT practice questions to get used to the phrasing. Time yourself: function problems should take under 2 minutes each. After solving, review the rule again to see if you missed any nuance. For more practice, check out our functions page.