If f is a function, then this means that one input cannot produce more than one output. This is an algebraic version of the vertical line test. To put it another way, in the graph of a function, no point on the graph can be directly above or below another point on the graph because that would entail having one x value that can yield two or more different y values.
Now consider the information given. We are told that there are two function values (which can be interpreted as y values), and one is greater than the other. In other words, they are not equal. So one is higher on the coordinate plane than the other. Given that, then they cannot have the same x value. If they did, then one would be directly above the other, and it would fail the vertical line test and not be a function.
So a≠b must be true.
The wording of the question seems to leave open the possibility of more than one correct answer. So all need to be considered. The given information doesn't really tell us much. We can't tell if f is an increasing or decreasing function, where its x intercepts are or whether it even has x intercepts. So none of the other answer choice are knowable things, and the only answer is (a).
Aren B.
Thank you10/03/19