Answer :

Final answer:

The function f^-1(x) is equal to (x+3)/(x-2), where x is not equal to 3.

Explanation:

The question asks whether the function f^-1(x) is equal to x+2/x-3, where x is not equal to 3. To determine if this is true, we can follow these steps:

  1. Start with f(x) = x+2/x-3.
  2. Replace f(x) with y: y = x+2/x-3.
  3. Interchange x and y: x = y+2/y-3.
  4. Solve for y: y = (x+3)/(x-2).
  5. Replace y with f^-1(x): f^-1(x) = (x+3)/(x-2).

Therefore, the function f^-1(x) is indeed equal to (x+3)/(x-2), where x is not equal to 3.

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Rewritten by : Barada