Find a **bijection** between two intervals

Question

I am struggling with this question and was hoping somebody could help me, Thanks

Find a bijection between the intervals $(-1,1)$ and $(0,4)$ where $X \in R$

Answer 1

$f:(\color\red{-1},\color\green{1})\rightarrow(\color\orange{0},\color\purple{4})$

$f(x)=(x-(\color\red{-1}))\cdot\frac{\color\purple{4}-\color\orange{0}}{\color\green{1}-(\color\red{-1})}+\color\orange{0}=2x+2$

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$g:(\color\orange{0},\color\purple{4})\rightarrow(\color\red{-1},\color\green{1})$

$g(x)=(x-\color\orange{0})\cdot\frac{\color\green{1}-(\color\red{-1})}{\color\purple{4}-\color\orange{0}}+(\color\red{-1})=\frac12x-1$