How do I determine and state the definition of f(x+Δx)=?

You are given a function f(x). If you are asked to determine f(y), all you need to do is substitute y for x in the definition of the function.
 
The problem says "Determine \(\displaystyle f(x+ \Delta x)\) for the given function" but you don't show any "given" function.

It also says "(c) State the given function" so it looks like you were "given" a function somewhere else.
 
You appear to have not copied all of the problem. When it says "the given function" there must be some place where there is an actual, specific function.
 
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