We might guess that the point (1,1) is a solution, but without anything regarding function g(x) other than a partial graphical representation, we have no way to check our answer.
Secondly, by the inclusion of choice (4), a guess could be made that the graph given in the question was intended to be parabolic and that the student was supposed to take an educated guess at the coordinates for a few of its points so as to derive a quadratic function. There is nothing in the question to rule out a situation such as this:
The function in red as shown here agrees with everything that is given in the problem. In this case, none of the four choices can be accepted as a solution.
In this question any answer chosen by a student would be incorrect. To expect any student to reason out an answer would be encouraging them to base arguments on unknown information and would be encouraging them to make convenient but unsupported assumptions in the absence of facts.