## Mappings between intervals

Find functions that map:

• #### Variant 1

The interval $$(0{,}1)$$ to the interval $$(0,\infty)$$.

• #### Variant 2

The interval $$(0{,}1)$$ to the interval $$(-\infty,\infty)$$.

• #### Variant 3

The interval $$(0{,}1)$$ to the interval $$\langle0{,}1\rangle$$.

• #### Variant 4

The interval $$\langle 0{,}1\rangle$$ to the interval $$\langle 0,\infty)$$.

• #### Variant 5

The interval $$(0,\infty)$$ to the interval $$(0{,}1)$$.