PSAT Math Grid-Ins Question 14: Answer and Explanation

Question: 14

If f(x) = x² - x + 4, a is non-negative, and f(a) = 10, what is the value of a?

Correct Answer: 3

Explanation:

3

The question asks for the value of a function. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Therefore, x = a and f(x) = f(a) = 10. Plug x = a into the function to get f(a) = a² - a + 4. Since f(a) = 10, replace f(a) with 10 to get 10 = a² - a + 4. To solve for a, subtract 10 from both sides of the equation and factor. The equation becomes 0 = a² - a - 6, which can be factored into 0 = (a - 3)(a + 2). Set both factors equal to 0 to get a = 3 or a = -2. There are two possible solutions to this equation, but the question states that a is non-negative, so -2 cannot be a solution. The correct answer is 3.