Answer:
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)