There are a great many functions that fail the horizontal line test which we nevertheless seem to have inverse functions for. For example, x^2 fails HLT but the square root of x is a pretty reasonabl...There are a great many functions that fail the horizontal line test which we nevertheless seem to have inverse functions for. For example, x^2 fails HLT but the square root of x is a pretty reasonable inverse for it – one just needs to be careful about the “plus or minus” issue. This apparent contradiction can be resolved using the notion of restriction.