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

Question

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

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Answer 1 · 2018-05-21T18:34:28

Shown below

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