Given, f(x)=|x−2|+|x−3| We know that for f(x)=|x−a|+|x−b|, the minimum value of f(x), we get either at x=a or at x=b So for f(x)=|x−2|+|x−3| f(2)=0+1=1,f(3)=1+0=1 So, f(x)min=1 and maximum value will be ∞ at x=∞. ∵fmax=∞+∞=∞ So, range =[1,∞)