Many of my algebra and precalculus students think the 'inverse function' of f(x), often written f^(-1)(x), is the same as the reciprocal 1/f(x) (mistaking the -1 for an exponent). This (as I am obliged to remind them) is almost always false. But can you find at least one function whose inverse is also its reciprocal? Tiebreaker: Find as many as you can!

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