question_answer 23)

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.       (i)    defined by f(x) = 3 ? 4x       (ii)    defined by f(x) = 1 + x2  

Answer:

(i)  defined by f(x) = 3 ? 4x             Let  x1, x2 be such that f(x1) = f(x2)              is one ? one.       Let  be any real number.        f(x) = y                    Corresponding to every element  there exists             (ii) f :  defined by f(x) = 1 + x2       Let x1, x2  be such that f(x­1 = f(x2)                                is not one-one.             As        Range of f is greater than or equal to 1              is not onto.       Thus, f is neither one-one nor onto.