15 pts. prove that the function f from r to (0, oo) is bijective if - f(x)=x2 if r- hint: each piece of the function to "cover" information to break your proof(s) into cases. part of (0, you may want to use this

Answer with explanation:

Given the function f from R  to

f:

To prove that  the function is objective from R to  

Proof:

When we prove the function is bijective then we proves that function is one-one and onto.

First we prove that function is one-one

Let

Cancel power on both side then we get

Hence, the function is one-one on domain [tex[(0,\infty)[/tex].

Now , we prove that function is onto function.

Let - f(x)=y

Then we get

The value of y is taken from

Therefore, we can find pre image  for every value of y.

Hence, the function is onto function on domain

Therefore, the given is bijective function on not on  whole domain  R .

Hence, proved.