SAT Math Multiple Choice Question 738: Answer and Explanation

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Question: 738

3. If g(x + 1) = x2 + 2x + 4 for all values of x, which of the following is equal to g(x)?

  • A. x2 + 4
  • B. x2 + 3
  • C. (x - 1)2 + 4
  • D. (x - 1)2 + 3

Correct Answer: B

Explanation:

B

Advanced Mathematics (functions) MEDIUM-HARD

Since the function takes "all values of x," one way to solve this problem is to choose a value of x to work with, like x = 1.

Original function:

g(x + 1) = x2 + 2x + 4

Substitute x = 1:

g(2) = (1)2 + 2(1) + 4 = 1 + 2 + 4 = 7

Therefore, the function g(x) will give an output of 7 for an input of 2. We can now test our choices for an input of x = 2. (Notice g(x) and g(x + 1) have different inputs.)

(A) (2)2 + 4 = 8

(B) (2)2 + 3 = 7

(C) (2 - 1)2 + 4 = 5

(D) (2 - 1)2 + 3 = 4

Notice that only the expression in (B) gives the correct output.

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