To determine whether the inverse of a function is a function you can perform the horizontal line test

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Yes indeed,

Use the Horizontal Line Test to determine whether a function is one-to- one. A function is one-to-one if and only if no horizontal line intersects its graph more than once. Example: From the graph at the left, determine whether the function is one- to-one and thus has an inverse that is a function.

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31 is prime. and it’s prime factorization is just 31.