whether each of these functions is a bijection from R to R. f (x) = x 3 -1
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Consider the function Let us show that this function is an injection. Let Then and hence It follows that and is an injective function. Further, let us show that this function is a surjection. Since for any the equation is equivalent to and hence has the solution we conclude that is a surjection. Consequently, the function is a bijection.