The mapping f:R->R defined by f(x)=|x|: 1) One one onto 2) One one into 3) Many one into 4) None of these

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember the definition of absolute value function such that:

`f(x) = |x| = {(x, x>=0), (-x, x<0):}` 

Notice that for each element in domain of the given function there exists an element in the range of given function, hence, the absolute value function is an into function.

You also need to notice that different inputs produce the same output such that:

`x = 3 => f(x) = |x| = |3| = 3`

`x = -3 => f(x) = |x| = |-3| = -(-3) = 3`

Hence, different inputs `x = 3`  and `x = -3`  produce one output `f(x) = 3` , hence, the function is called many to one function.

Hence, evaluating the given absolute function yields that this is a many to one into function, hence, you need to select the answer 3.