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Q EXAMPLES 8. If ƒ : R  R be defined as follows :

                                           ƒ (x) =  1 , i f x Q - 1 , i f x Q

          Find (i) ƒ (1/2), ƒ ( π ), ƒ  2                    (ii) Range oƒƒ                 (iii) pre- images oƒ 1 and – 1.


Dear Student,
Please find below the solution to the asked query:

We havefx=1,ifxQ-1,ifxQi.e.fx=1,ifxRational Number-1,ifxIrrational NumberAs 12 is rational number, hencef12=1As π and 2 are irrational number hencefπ=-1f2=-1As clear from function definition, range of function is -1,1As functional value of 1 is achieved for rational numbers and -1 is acheived for irrational numbers, hencepre-image of 1 is all rational numbers and pre-image of -1 is all irrational numbers.

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