SAT Math Multiple Choice Question 657: Answer and Explanation

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Question: 657

12. If h and k are functions such that h(x) = x + 3 and h(g(2)) = 9, which of the following could describe g(x)?

  • A. x2 + 2
  • B. x2 + 3
  • C. x2 + 4
  • D. x2 + 5

Correct Answer: A

Explanation:

A

Advanced Mathematics (functions) MEDIUM-HARD

Given:

h(g(2)) = 9

Apply definition h(x) = x + 3:

g(2) + 3 = 9

Subtract 3:

g(2) = 6

Therefore, g must be a function that takes an input of 2 and gives an output of 6. The only choice that satisfies this condition is (A) g(x) = x2 + 2, because g(2) = (2)2 + 2 = 4 + 2 = 6.

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