Question

The function g(x) is the inverse of the function f (x) = (x + 1)2 + 2, when x < -1

Answer 1

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Answer:

  g(x) = -√(x -2) -1

Step-by-step explanation:

We note the domain of f(x) is x ≤ -1. The is the range of the function g(x).

The inverse function is the solution to ...

  x = f(y)

  x = (y +1)² +2

  x -2 = (y +1)²

  -√(x -2) = y +1 . . . . . . . we are interested only in the negative values

  y = -√(x -2) -1

The inverse function is ...

  g(x) = -√(x -2) -1