# SAT Math Multiple Choice Question 924: Answer and Explanation

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**Question: 924**

**8.** If *g*(*x* + 3) = *x*^{2} + 2*x* + 1, then which of the following gives *g*(*x*)?

- A.
- B.
- C.
- D.

**Correct Answer:** B

**Explanation:**

**B**

**Difficulty:** Hard

**Category:** Passport to Advanced Math / Functions

**Strategic Advice:** The key to answering a question like this is having a conceptual understanding of function notation. Here, the input (*x* + 3) has already been substituted and simplified in the given function. Your job is to determine what the function would have looked like had *x* been the input instead.

**Getting to the Answer:** To keep things organized, let *u* = *x* + 3, the old input. This means *x* = *u* - 3. Substitute this into *g*(*x* + 3) and simplify:

This means *g*(*u*) = *u*^{2} *-* 4*u* + 4. Now, when working with function notation, you evaluate the function by substituting a given input value for the variable in the parentheses. Here, if the input value is *x*, then *g*(*x*) = *x*^{2} - 4*x* + 4, which is (B).