Find the inverse of the function on the given domain.

Question

 f (x) = (x + 1)^2 − 3, [−1, ∞)

Answer 1

The given function is the right half of a parabola opening upward with vertex (-1,-3).

So, domain = [-1, infinity) and range = [-3, infinity)

To find the inverse function:

Step 1: set y = f(x)

y = (x+1)^2 - 3

Step 2: switch x and y

x = (y+1)^2 - 3

Step 3: solve for y

(y+1)^2 = x+3

y+1 = +/- sqrt(x+3)

y = -1 +/- sqrt(x+3)

Since the domain of f(x) is [-1, infinity), so is the range of f^-1(x).

Therefore f^-1(x) = -1 + sqrt(x+3)