PSAT Math Multiple-Choice Question 201: Answer and Explanation

Question: 201

x	- 2	- 1	0	1	2	3
g(x)	5	3	1	- 1	- 3	- 5
h(x)	- 3	- 2	- 1	0	1	2

Several values for the functions g(x) and h(x) are shown in the table above. What is the value of g(h(3))?

• A. - 5
• B. - 3
• C. - 1
• D. 2

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Passport to Advanced Math/Functions

Getting to the Answer: The notation g(h(x)) indicates a composition of two functions, which can be read "g of h of x." It means that the output when x is substituted in h(x) becomes the input for g(x). First, use the top and bottom rows of the table to find that h(3) is 2. This is your new input. Now, use the top and middle rows of the table to find g(2), which is -3, so (B) is correct.