1( below is the pre image dilate by a factor of 2
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Assuming the function is
For
to be differentiable, it necessarily has to be continuous. For this condition to be met, we need
For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have
Now we solve for
and 
:
For
For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have
Now we solve for