Find the range of each function . For any function that is not one to one , give two distinct values of x which have the same image .
(1) , x are real numbers
(2) , ,
(3) ,
the range for sine function is [-1,1]
but for the rest , i am not really sure .
(1) You know that sin x is periodic with period . That should give you an easy answer.
(2) This is a little harder because this is one to one. I would show that by arguing that the derivative is always positive and so the function is increasing but I don't know what methods you have available.
(3) I don't recognise "In(x)". Do you mean the natural logarighm? That is ln(x)- "logarithm" starts with a "l" not "I"! If so, same comments as in (2) apply.