What is the formula of the function that generalizes 1-x with concave and convex curves?

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Suppose there is a function f(x,alpha) such that alpha is its parameter. For each value of alpha I need to obtain one of the curves depicted below.

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I need to know the formula of this function. The function 1-x is a special case of this function that is shown in red. The domain and range of this function is [0,1].

Any ideas?