Q11 of 99 Page 53


Show that f is many-one and into.


To prove: function is many-one and into



We have,


f(x) = 1 when x is rational


It means that all rational numbers will have same image i.e. 1


⇒ f(2) = 1 = f (3) , As 2 and 3 are rational numbers


Therefore f(x) is many-one


The range of function is [{-1},{1}] but codomain is set of real numbers.


Therefore f(x) is into


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