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Is the inverse of a function always a function?explain
The inverse of a function may not always be a function! The original function must be a one-to-one function to guarantee that its inverse will also be a function. A function is a one-to-one function if and only if each second element corresponds to one and only one first element. (Each x and y value is used only once.)
The inverse is not a function: A function's inverse may not always be a function. The function (blue) f(x)=x2 f ( x ) = x 2 , includes the points (−1,1) and (1,1) . Therefore, the inverse would include the points: (1,−1) and (1,1) which the input value repeats, and therefore is not a function.
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