PSAT Math Multiple-Choice Question 415: Answer and Explanation

Question: 415

x	g(x)
-4	0
-3	2
-2	4
-1	6
0	8
1	10

x	h(x)
-2	- 4
-1	2
0	0
1	-2
2	- 4

Several values for the functions g(x) and h(x) are shown in the tables above. What is the value of g(h(-2))?

• A. -2
• B. 0
• C. 4
• D. 10

Correct Answer: B

Explanation:

B

Difficulty: Medium

Strategic Advice: The notation (g(h(x)) can be read "g of h of x." It means that when x is substituted into h(x), the output becomes the input for g(x).

Getting to the Answer: Start with the innermost function. Use the h(x) table to find h(-2); when x = -2, the output h(x) = -4. Use -4 as the input for g(x) to find g(-4) from the g(x) table. When x = -4, the output g(x) = 0. Choice (B) is correct.