QUANTITATIVE REASONING · GMAT-Q-FUN

Functions, Inputs and Outputs

GMAT lesson development preview · DRAFT · Original learning and assessment material

Concepts and problem-solving strategy

Core mathematical relationship

f (x) = 2 x^{2} - 3

Translate the condition

A function assigns one output to each input. Substitute the requested input into the rule, then simplify in the stated order.

Test the result

Check the input and output separately. In a composition, evaluate the inside function first; changing the order changes the result.

Think Like a GMAT Test-Taker

Evaluate the innermost input first and preserve the order of composition.

Faster Methods

Translate the target into an equation before calculating.

Check the result against the original conditions and units.

Worked example 1

The function f is defined by f(x)=2x²−3. What is f(2)?

f (2) = 2 (2^{2}) - 3 = 5

Substitute 2 into the function rule: square the input, multiply by 2, and subtract 3, giving 2(4) - 3 = 5.

Worked example 2

For f(x)=4x+7, find the input whose output is 31.

4 x + 7 = 31 ⟹ 4 x = 24 ⟹ x = 6, f (6) = 31

An output question substitutes a known input; an input question sets the rule equal to the requested output. Undo addition before multiplication and verify the input in the original rule.

Worked example 3

For f(x)=x squared and g(x)=x+2, compare f(g(3)) and g(f(3)).

f (g (3)) = f (5) = 25, g (f (3)) = g (9) = 11

Follow the inside operation first. Reversing the order changes which quantity is squared: the first calculation squares five, while the second adds two after squaring three. Composition is not generally interchangeable.

Common Traps

Keep domain restrictions after simplifying.
Do not confuse the requested output with an intermediate quantity.