Question

The function `f` is defined by `f(x)=1-x^2`, `x sub RR`. Show that `f` is NOT one-to-one. Can someone help me please?

The function `f` is defined by `f(x)=1-x^2`, `x sub RR`.
Show that `f` is NOT one-to-one.

Answer 1

Shown below

Explanation:

Its many to one

`f(-1) = f(1) = 0`

Hence there are multiple `x` that gives the same `f(x)`

In a one to one, there is only one `x` for each `f(x)`

Hence this function actually represents many to one, hence not one to one