Which of the following are one-one ,onto (or) bijections? Justify your answer.
(i) `f: R to R, f(x) =(2x+1)/3`
(ii) `f: N to N, f(x) = 2x+3`
(iii) `f:[0, infty) to [0,infty), f(x) = x^(2)`
(iv) `f: R to R, f(x) =x^(2)`
(v) `f: R to (0, infty), f(x) = 5^(x)`
(vi) `f: (0, infty) to R, f(x) = log_(e)^(x)`
(vii) `f: R to R, f(x) = {{:(x, if x gt 2),(5x-2, if x le 2):}`

Answer

(i) bijection, (ii) injection but not a surjection, (v) Neither injection nor surjection,
(vi) bijection, (vii) bijection, (viii) onto but not one-one