Let f be a continuous function satisfying `f '(l n x)=[1` for `0< x<= 1, x` for `x > 1` and `f (0) = 0` then `f(x)` can be defined as
(a)`f(x)={(1 , "if"x le 0 ),(1-e^(x), "if" x gt 0 ):}` `" "`(b)`f(x)={(1,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}`
(c)`f(x)={(x,"if" x lt 0),(e^(x),"if" x gt 0 ):}` `" "`(d)`f(x)={(x,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}`

Options

A. `f(x)={(1 , "if"x le 0 ),(1-e^(x), "if" x gt 0 ):}`
B. `f(x)={(1,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}`
C. `f(x)={(x,"if" x lt 0),(e^(x),"if" x gt 0 ):}`
D. `f(x)={(x,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}`

Answer

D