# SAT Math Multiple Choice Question 738: Answer and Explanation

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**Question: 738**

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

- A.
*x*^{2}+ 4 - B.
*x*^{2}+ 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) = *x*^{2} + 2*x* + 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.