In the above question given for all x the belonging to R expression takes all real values how will this be affected by value of p ? Could u pl find range of p and even explain the justification for onlythose values of p the given question satisfies

Excepts for p=2 or 1 if we plot the curve we have one local minimum and one local maximum the region between whom is the one which does not come in range and hence if the local maximum> local minimum we can find this range.
So now basicall you have to differentiate this and solve for the two x in terms of p and then put it back in the original equation and check the difference between maximum and minimum and make it greater than zero, which will give you a range.
Hope you dont mind me not solving such tedious task, I have already given you a direction to approach this problem