# 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.
*x*^{2}+ 2 - B.
*x*^{2}+ 3 - C.
*x*^{2}+ 4 - D.
*x*^{2}+ 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)* = *x*^{2} + 2, because *g*(2) = (2)^{2} + 2 = 4 + 2 = 6.