What is the inverse of `f(x) = 1/(x - 2) + 3`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The inverse of the function `f(x) = 1/(x - 2) + 3` has to be determined. For a function f(x), the inverse `f^-1(x)` is related by `f(f^-1(x)) = x`

For `f(x) = 1/(x - 2) + 3`

`f(f^-1(x)) = 1/(f^-1(x) - 2) + 3 = x`

=> `1/(f^-1(x) - 2) = (x - 3)`

=> `1/(x - 3) = (f^-1(x) - 2)`

=> `f^-1(x) = 1/(x - 3) + 2`

The inverse of `f(x) = 1/(x - 2) + 3` is `f^-1(x) = 1/(x - 3) + 2`

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