Find homeomorphism between sets

1 - $\displaystyle \left[ {a,\infty } \right[\& \left[ { - 1,1} \right[$

2- $\displaystyle \left] { - \infty ,1} \right]\& \left] { - 1,1} \right]\,

$

is the solution

$\displaystyle \begin{array}{l}

f_1 \left( x \right) = \frac{{x - 2a}}{x} \\

f_2 \left( x \right) = \frac{{2 - x}}{x} \\

\end{array}

$