Final answer:
The inverse of the function f(x)=√x-6 is f^(-1)(x) = x² + 6. The domain of the inverse function is x ≥ -6.
Step-by-step explanation:
To find the inverse of a function, we switch the roles of x and y and solve for y. For the function f(x)=√x-6, let's start by replacing f(x) with y:
y = √x-6
Now, let's switch x and y:
x = √y-6
To solve for y, we need to isolate it on one side of the equation:
y-6 = x²
y = x² + 6
So, the inverse of f(x) is f^(-1)(x) = x² + 6.
The domain of the inverse function is the same as the range of the original function. Since the range of f(x) is y ≥ -6, the domain of the inverse function is x ≥ -6.