Soon. i have been stuck on this algebra 1 question for what feels like an eternity can someone and soon?

You are trying to find an x-value for which f(x) = g(x).  At first your choice of x is arbitrary.  In the given table, the first x-value tried was 0 (zero).  For this value of x, f(x) does NOT equal g(x).

Next x was 1.  f(x) and g(x) are even further apart here.  So reject 1 and try 2 instead.  Notice how f(x) and g(x) are closer together now than they were for x=1.

Note that for x=2.5, f(x) and g(x) are even closer together; ony 0.75 separates them.   

Your turn.  Try x=2.4, x=2.3, and so on.  You may have to go in the other direction:  Try x=2.6, x=2.7, and so on.  If f(x) and g(x) are getting closer to one another, you're going in the right direction; if further apart, you're going in the wrong direction.  

Have fun.  This really is an interesting problem.

The correct answer is .44