Express `f(x) = |1/(2x) - 2| - |1/(2x) + 2|` in the non-modulus form?

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The function `f(x) = |1/(2x) - 2| - |1/(2x) + 2|`

`|x|` is equal to x if `x>=0` and it is equal to `-x` if `x < 0`

`f(x) = |1/(2x) - 2| - |1/(2x) + 2|`

If `x >= 1/4` , `f(x) = 1/(2x) - 2 - 1/(2x) -...

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The function `f(x) = |1/(2x) - 2| - |1/(2x) + 2|`

`|x|` is equal to x if `x>=0` and it is equal to `-x` if `x < 0`

`f(x) = |1/(2x) - 2| - |1/(2x) + 2|`

If `x >= 1/4` , `f(x) = 1/(2x) - 2 - 1/(2x) - 2 = -4`

If `x <= -1/4` , `f(x) = -1/(2x) + 2 + 1/(2x) + 2 = 4`

If `-1/4 < x <1/4` , `f(x) = 2 - 1/(2x) - 1/(2x) - 2 = -1/x`

The function `f(x) = |1/(2x) - 2| - |1/(2x) + 2|` is the same as `f(x) = [[-4, x >= 1/4],[-1/x, 1/4 > x > -1/4],[4, x<= -1/4]]`

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