Solution
= Solution
\b[Not <injective>; <surjective>.] The equal values $f(0)=f(2)=1$ disprove <injectivity>. For any $y>0$, take $x=1+y^{-1/2}>1$. This lies in the stated <domain of a function>, and
$$
\frac1{(1-|x|)^2}=\frac1{(-y^{-1/2})^2}=y.
$$
Consequently every member of the <codomain> has a <preimage>.