These are exam papers and I'm studying for a junior cert so the textbook doesn't give the same kind of questions.

So do you think I'd still get the marks if I estimated 0.8 or 0.7 because **I thought there would be some formula** to get the 0.77 like when you get the table of values

Since the problem says to "use your graphs to answer ... estimate a third value", clearly they don't want you to use a formula.

You could make a table of values as you did, and when you find the answer is between

**-**0.8 and

**-**0.7, then make a table by hundredths over just that interval; but they didn't say they wanted the nearest hundredth, so why bother?

Don't expect more of yourself than the problem states. Read carefully.

I don't get the terms you used there for the notation because I honestly haven't heard them till now but the sentence in words at the bottom makes more sense. Would it be okay if I wrote

X is 2^x > x² in the range {0.8<X<2} and {X>4}, X is an element of R

They didn't say what form the answer should take, so just writing in words something like "x can be between about

**-**0.8 and 2, or greater than 4" would probably be fine. What you wrote might be better.

But if this is a sample problem from the maker of the exam, and they imply, as they do, that they expect you to know set-builder notation, then you may want to study it ...