Final answer:
The inverse function of f(x) is f^(-1)(x) = √(11 - x). The domain of f^(-1)(x) is x ≤ 11.
Step-by-step explanation:
The inverse function of f(x) can be found by swapping the x and y variables and solving for y. So, to find f^(-1)(x), we will let y = f^(-1)(x) and solve for x.
Start by replacing f(x) with x in the equation for f(x):
x = 11 - y^2
Next, rearrange the equation to solve for y:
y^2 = 11 - x
Then, take the square root of both sides:
y = ±√(11 - x)
Since x >= 0, we consider only the positive square root:
f^(-1)(x) = √(11 - x)
Therefore, the domain for f^(-1)(x) is all real numbers such that 11 - x ≥ 0, which simplifies to x ≤ 11.