Which function has an inverse that is also a function?

A function has an inverse that is also a function only if it is one-to-one: different inputs must give different outputs. The function g(x) = 2x − 3 is a nonhorizontal line, so each output comes from exactly one input. The absolute-value function and the squared function give the same output for some different inputs, while w(x) = −20 is constant, so those do not have function inverses.

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