How to correct a variable?

Question

Mathematics

There is a variable from the position sensor
Changes in the range 0 to 1
Average position 0.5
Sensor sensitivity near 0.5 high
closer to the edges, that is, to 1 and 0 - low
how to choose a function for the variable to increase sensitivity
closer to the edges
tell me where to dig

Answer 1

Take the parabola, for example. The top at the point (0.5;1) - there is no amplification in the center. At 0 and 1, for example, gain 2 is needed, then the equation
f=(x-0.5)*(x-0.5)*(4*( 2 - 1 )) + 1
2 are the values ​​at the edges of the range (0 and 1)
1

is the value in the middle of the range (0.5 )

Answer 2

Gauss bell