Consider the function and its inverse. f of x is equal to x squared plus 4 and f inverse of x is equal to negative square root of x minus 4 end root When comparing the functions using the equations, which conclusion can be made?

The inverse is f⁻¹(x) = −√(x − 4), so its input must satisfy x − 4 ≥ 0, or x ≥ 4. Because the inverse uses the negative square-root branch, the original function f(x) = x² + 4 must be restricted to inputs x ≤ 0. Therefore, the correct conclusion is that the domain of f is x ≤ 0 and the domain of f⁻¹ is x ≥ 4.

AI-written and checked against the verified answer.