We note that there are point, x1 and x2 with x1 ≠ x2 and f (x1) = f (x2), for instance, if we take x1 = 2 and x2 = 1/2, then we have f (x1) =2/5 and f (x2) =2/5 but 2 ≠ 1/2 Hence f is not oneone Also, f is not onto for if so then for 1∈R ∃ x ∈ R such that f (x) = 1 which gives x/ (x21) =1The function f R → R defined by f(x) = 2x 1 is surjective (and even bijective), because for every real number y, we have an x such that f(x) = y such an appropriate x is (y − 1)/2 The function f R → R defined by f(x) = x 3 − 3x is surjective, because the preimage of any real number y is the solution set of the cubic polynomialIs x^3 x onetoone and onto?
Pdf 01 Sets Relations And Functions Himanshu Gautam Academia Edu