If f(x) = x2 -1, what is the equation for f–1(x)?

Step-by-step explanation:

That's f(x) = x^2 - 1, where the " ^ " indicates exponentiation.

To find the inverse function of f(x):

1.  Replace "f(x)" with "y":  y = x^2 - 1

2. Interchange x and y:  x = y^2 - 1

3.  Solve this result for y:   y^2 = x + 1 or y = +√(x + 1).

    Important:  the inverse of the given function is defined only on the   domain [-1, infinity), since the argument x + 1 MUST be ≤ 0.  Also, because a relationship is a function ONLY if there is only 1 value of y for each value of x.  That's why the inverse function is +√(x + 1) and not ±√(x + 1).

4.  Finally, label the inverse function by replacing "y = " with

   -1

"f    (x) = ":

  -1

f    (x) = +√(x + 1)

1. perpendicular

2. parallel

3. perpendicular