PSAT Math Multiple-Choice Question 427: Answer and Explanation

Question: 427

If f(x) = -x + 5 and g(x) = x², which of the following is NOT in the range of f (g(x))?

• A. -11
• B. 0
• C. 1
• D. 9

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Function Notation

Getting to the Answer: When dealing with a composition (or nested functions), the range of the inner function becomes the domain of the outer function, which in turn produces the range of the composition. In the composition f (g(x)), the function g(x) = x² is the inner function. Every value of x, when substituted into this function, will result in a nonnegative value (because the value of x is squared). This means the smallest possible range value of g(x) is 0. Now, look at f(x): substituting large positive values of x in the function will result in large negative numbers. Consequently, substituting the smallest value from the range of g, which is 0, results in the largest range value for the composition, which is -0 + 5 = 5. Therefore, the range of f(g(x)) is ≤ 5. The only answer choice that does not fall within this range is (D).