Inverse function: Difference between revisions

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For a function <math>f\colon X\to Y</math>, its inverse <math>f^{-1}\colon Y\to X</math> admits an explicit description: it sends each element <math>y\in Y</math> to the unique element <math>x\in X</math> such that {{Math|1=''f''(''x'') = ''y''}}.

As an example, consider the

As an example, consider the [[Real number|real-valued]] function of a real variable given by {{math|1=''f''(''x'') = 5''x'' − 7}}. One can think of {{Mvar|f}} as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of {{Mvar|f}} is the function <math>f^{-1}\colon \R\to\R</math> defined by <math>f^{-1}(y) = \frac{y+7}{5} .</math>

As an example, consider the [[Real number|real-valued]] function of a real variable given by {{math|1=''f''(''x'') = 5''x'' − 7}}. One can think of {{Mvar|f}} as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of {{Mvar|f}} is the function <math>f^{-1}\colon \R\to\R</math> defined by <math>f^{-1}(y) = \frac{y+7}{5} .</math>

==Definitions==