Question

Having a little trouble with it:

Is \(f(x) = \dfrac{2x}{1+x^2}\) an injective? Why or why not?

If I graph this function, we can see that it is not injective, but how to show that algebraically?

Answer 1

@ganeshie8 @iGreen @AriPotta

Answer 2

OK, we start with \(f(a) = f(b)\)

I am stuck at \(b+a^2b = a+ab^2\)...

I honestly don't know how to show that it is not injective without depending on graph.

Answer 3

what is \[f(1/x)\]

Answer 4

We can go from there: