How to compensate for a filter if the transfer function is known

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I am rather new to filter design. I just want to apply the inverse of a simple 4th order Butterworth low pass filter to a given signal and then apply the Butterworth filter to the compensated signal to see that I get out my original signal. The signal I am using to test on has frequency components far below the corner frequency. The final result of applying the inverse of the filter and then applying the filter does not result in my simple code in the original signal (code attached). Can someone explain this to me?

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