PSAT Math Multiple-Choice Question 181: Answer and Explanation

Question: 181

If f(g(2)) = -1 and f(x) = x + 1, then which of the following could define g(x)?

• A. g(x) = x - 6
• B. g(x) = x - 4
• C. g(x) = x - 2
• D. g(x) = x - 1

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Passport to Advanced Math/Functions

Getting to the Answer: Understanding the language of functions will make questions that seem complicated much more doable. When you know the output of a function (or in this question, a composition of two functions), you can work backward to find the input. Because g(x) is the inside function for this composition, its output becomes the input for f(x). Unfortunately, you don't have any information about g yet. You do know, however, that f of some number, g(2), is -1, so set f(x) equal to -1 and solve for x:

You now know that f (-2) = -1. In the equation for the composition, g(2) represents x, so you also know that g(2) must be -2. Your only option now is to use brute force to determine which equation for g, when evaluated at 2, results in -2.

(A): g(2) = 2 - 6 = -4 (not -2), eliminate.

(B): g(2) = 2 - 4 = -2

You don't need to go any further; (B) is correct.

You could check your answer by working forward, starting with g(2):