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Quiz 5
One-to-one or not?
1. $\left\{ \begin{array}{ll}
f \colon \mathbb{R} \rightarrow \mathbb{R} \\
f(x)=x^2
\end{array} \right.$
Not one-to-one because, for example, $f(-1)=f(1)$ while $-1 \neq 1$.
2. $\left\{ \begin{array}{ll}
f \colon [-1,0] \rightarrow \mathbb{R} \\
f(x)=x^2
\end{array} \right.$
Yes, it is one-to-one.
3. $\left\{ \begin{array}{ll}
f \colon [0,1] \rightarrow \mathbb{R} \\
f(x)=x^2
\end{array} \right.$
Yes, it is one-to-one.
4. $\left\{ \begin{array}{ll}
f \colon \mathbb{N} \rightarrow \mathbb{N}_0 \\
f(x)=x^2
\end{array} \right.$
Yes, it is one-to-one.
5. $\left\{ \begin{array}{ll}
f \colon \mathbb{Z} \rightarrow \mathbb{R} \\
f(x)=x^2
\end{array} \right.$
No, it is not one-to-one because, for example, $f(-1)=f(1)$ while $-1 \neq 1$.
