I need help with these questions can someone please help me

I need help with these questions can someone please help me?

I Is Rfnetion from AoDefiud yr swer) 2. In each cao, giw, nn cornrl\" d b functinn with the stated proomaa. It is onto but it s sot one-to-one (e) It is one to-one and it is also oato.

Solution

a) f(x) = 2x from the set of natural numbers N to N is NOt onto, because, for example, nothing in N can be mapped to odd numbers by this function.

    f(x1) = f(x2)

     2x1 = 2x2 => x1 = x2

    Therefore the function is one one.

b) g (x) = | x - 2 |, g: R -> [0, infinity)

This absolute value function has y-values that are paired with more than one x-value, such as (4, 2) and (0, 2).
This function is not one-to-one.

the function is ONTO because for all values of g(x) there is atleast one value of x such that g (x) = | x - 2 | .

c) f (x) = 3x - 4 f: R -> R

   This function (a straight line) is ONTO because as you progress along the line, every possible y-value is used

In addition, this straight line also possesses the property that each x-value has one unique y-value that is not used    by any other x-element. so its one to one function.