Advanced MathHardInputs that give a stated output
Advanced Math practice question
The function f is defined by f(x) = 3(x − 1)² + 2. For what values of x does f(x) = 14, and what is their sum?
Answer: 2
3(x − 1)² + 2 = 14 gives 3(x − 1)² = 12, so (x − 1)² = 4 and x − 1 = ±2. The inputs are x = 3 and x = −1, and their sum is 2.
Common wrong answers
- If you answered 3
- 3 is only the larger input; the other is −1.
- If you answered 4
- 4 is (x − 1)², one step before the roots; the inputs themselves are 3 and −1.
- If you answered -1
- −1 is only the smaller input.
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