Unusual Linear Mapping??

Dear list,

I need to perform an unusual linear mapping as follows -

I have a control which ranges from 0 - 1.

When the control is at 0 I want the value to be 0

When the control is at 0.5 I want the value to be
0.94117647058823529411764705882353

When the control is at 1 I want the value to be 1

Summarized -

0 - 0
0.5 - 0.94117647058823529411764705882353
1 - 1

Any ideas on how to perform this mapping or how to attempt to solve
it?

Thanks for any help,
David
.