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Consider f(x)= [x]+|| x-1|-2| . Find the number of solution(s) of the equation 3 f(f(x))-1=0 in [-2,4] . [Note: [y] and y denotes greatest integer function less than or equal to y and fraction part function of y respectively.]

Correct answer

6

Step-by-step solution

aligned & f(x)= [x]+|| x-1|-2| &= |x-1|-2 & 3 f(f(x))-1=0 f(f(x))= 1 3 aligned Let f(x)=t f(t)= 1 3 Number of values of t for which f(t)= 1 3

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