For d part , remember this method, shift x^2+x+1 to lhs and make a quadratic in x . then put D>=0 as x is real. In this way you get range of y.
For e part first make 5+4x-x^2>0 , and think as this term approaches zero the whole log term approaches -\infty. and as x approaches 5 it again approaches -\infty, so there is a particular value of x between 0 and 5 , where maxima occurs, to find that simply diffrentiate and put it equal to 0 .
you'll get x=2, y=2(value of the expression).
so range is (-\infty,2)
Ask if any doubts