Question

consider the reciprocal function f:R-nullset0-R-nullset0 defined by f of x =1/x.
a. show that f is bijective?
b. is f bijective if the domain R-nullset 0 is replaced by N​

Answer 1

Answer:We have for the given function which is defined as f(x) = 1/x, x € D(f) = R -{0} ;

(I) let f(x) = f(x’) for x, x’ belonging to D(f) ==> 1/x = 1/x’ ==> x = x’ and

(II) let y € co-domain of f i.e. R -{0} ==> y is not zero, then (1/y) = x € D(f) & x is not zero, such that f(x) = 1/x = y .

Therefore f is one-one & onto or bijective

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