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g(x) is not clear,because there is no indication what kind of non-linear function it is. IF it is assumed to be a quadratic (defined by three given points), then you can work back to get f(0) by forward differences. |dw:1439301717122:dw|
For a quadratic, the second difference is constant. so if we tabulate the differences, we can work out g(0).
i believe the answer is f(x)
I totally agree that it is a horrible question, which we see very often in multiple choice questions. Unfortunately today math does not teach students to be rigorous, but instead, (incorrectly in math ) to generalize.
sorry about that. but thanks everyone for your help :)
If it is cubic, it is NOT defined by three points. If it is quadratic, there is only one quadratic that passes through all these points.
IF it is a quadratic, then we can use the following table to work it out. Unfortunately with a multiple choice, you cannot support your answer in any way. That is why multiple choice questions are frustrating when the question is not properly made.
IF it is a quadratic, we can work backwards: |dw:1439302374183:dw| to conclude that g(0)=33