Consider, f(x)= |x-4| |x|+1 . If sum of all distinct possible values of ⁻¹( [f(x)]) is a +b then find the absolute value of (a+b) . [Note: [z] denotes greatest integer function less than or equal to z .]

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Correct answer: 5

Range of f(x) is [0,4] aligned ⁻¹( [f(x)]) & = ⁻¹( 0)+ ⁻¹( 1)+ ⁻¹( 2)+ ⁻¹( 3)+ ⁻¹( 4) & =0+1+ -2+ -3+ -4=3 -8 a +b (a+b) & =|3-8|=5 aligned

Consider, f(x)= |x-4| |x|+1 . If sum of all distinct possible values of ⁻¹( [f(x)]) is a +b then find the absolute value of (a+b) . [Note: [z] denotes greatest integer function less than or equal to z .]

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