SAT Math Multiple Choice Question 645: Answer and Explanation

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Question: 645

15. If f(x) = -x + 7 and g(f(x)) = 2x + 1, what is the value of g(2)?

  • A. -11
  • B. -5
  • C. 5
  • D. 11

Correct Answer: D

Explanation:

D

Advanced Mathematics (functions) HARD

Given function:

g(f(x)) = 2x + 1

Substitute f(x) = -x + 7:

g(-x + 7) = 2x + 1

To evaluate g(2), we must let -x + 7 = 2:

-x + 7 = 2

Subtract 7:

-x = -5

Multiply by -1:

x = 5

Substitute x = 5:

g(-5 + 7) = 2(5) + 1

Simplify:

g(2) = 11

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