The function #1/x^2# is always positive, and it increases without bound as x gets close to #0# and decreases toward zero as x gets bigger and bigger (whether positive or negative.)
You might know its graph:
graph{y=1/x^2 [-14.06, 14.42, -3.99, 10.25]}
Now in this question, the function is #f(x) = 5-1/x^2#.
Starting with #5#, we will subtract #1/x^2# which is a number greater than #0#, but with no upper bound.
That means at for some #x# we will subtract #500#, and for some other #x# we will subtract #5,000# and for another subtract #60,000# from #5#. (We will never subtract a negative, because #1/x^2# is never negative.)
The result of this subtraction will be at most #5# but for very large positive #1/x^2#, we will get very 'big' negatives, like #-100# and then #-10,000# and so on.
So, there is no lower bound for #f#.
Upper bounds
#f(x)# is bounded above (by every number greater than or equal to #5#) but is not bounded below. #5# is the least upper bound.
