If you meant what #2-(x+1)^(1/2)-x^2+4x-3# is between, then this solution is for you.
So, since #x# is a number greater than 0, we plug in 0 to the expression to get:
#2-(0+1)^(1/2)-0^2+4(0)-3#
#2-(1)^(1/2)-0+4(0)-3#
#2-1-0+0-3#
#-2#
This means that #2-(x+1)^(1/2)-x^2+4x-3# has to be greater than #-2#
Similarly, since #x# is a number smaller than 1, we plug in 1 to the expression to get:
#2-(1+1)^(1/2)-1^2+4(1)-3#
#2-(2)^(1/2)-1+4(1)-3#
#2-(2)^(1/2)-1+4-3#
#2-sqrt2#
Which is approximately #0.585786437627#. Therefore, #2-(x+1)^(1/2)-x^2+4x-3# has to be less than #2-sqrt2#
So we now have :#-2<2-(x+1)^(1/2)-x^2+4x-3<2-sqrt2#
