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4., , ., , 12., , Show that the Modulus Function f: R > R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if xis positive or 0 and |x| is — x, if x is negative., , Show that the Signum Function f: R > R, given by, , Lifx>0, f(x) =40 if x20, Lifx<0, , is neither onc-one nor onto., Let A= {1, 2,3}, B= (4,5, 6, 7} and let f= ((1, 4), (2, 5), (3, 6)} be a function, from A to B. Show that f is one-one., In cach of the following cases, state whether the function is one-one, onto or, bijective. Justify your answer., , (i) f: R > R defined by f(x) = 3 - 4x, , (ii) f: R @ R defined by f(x) = 1 +2¢, Let A and B be sets. Show that f: A x B + B x A such that f(a, b) = (b, a) is, bijective function., , n+! it nis odd, Let f: N — N be defined by f(n) = _ for alln € N., — ,if miseven, 2, State whether the function f is bijective. Justify your answer., Let A = R - {3} and B = R —- {1}. Consider the function f: A > B defined by, , fwe= (3) . Is f one-one and onto? Justify your answer., , , , Let f : R — R be defined as f(x) = x*. Choose the correct answer., , (A) fis one-one onto (B) fis many-one onto, , (C) fis one-one but not onto (D) fis neither one-one nor onto., Let f: R — R be defined as f(x) = 3x. Choose the correct answer., (A) fis one-one onto (B) fis many-one onto, , (C) fis one-one but not onto (D) fis neither one-one nor onto.