SAT Math Multiple Choice Question 345: Answer and Explanation
15. 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
Category: Passport to Advanced Math / Functions
Strategic Advice: Understanding the language of functions will make questions that seem complicated much more doable on Test Day. 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.
Getting to the Answer: 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.
Choice A: g(2) = 2 - 6 = -4 (not -2), so eliminate.
Choice 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):