PSAT Math Multiple-Choice Question 429: Answer and Explanation

Question: 429

Two functions are defined as follows: and . What is the value of g(f(x)) when x = 2?

• A. 6
• B. 12
• C. 34
• D. 36

Correct Answer: C

Explanation:

C

Difficulty: Easy

Category: Function Notation

Getting to the Answer: The trick to questions like this one is to make sure you're careful with the order of the nested functions. Work from the inside out. In this case, you're asked for g of f, so start with f(x), plugging in the given value for x: Now, move to the outer function:

This matches (C).

Note that if you had worked your nested functions in the wrong order—as you would if you'd been asked for f (g(x))—your final result would have been 6, which matches (A). Always double-check that you're working your way through nested functions in the correct order, from the inside to the outside.