For f(x) = –√(x – 5) – 2, what is the domain of f-1?Question 3Select one:a.(–∞, 2]b.[2, ∞)c.(–∞, –2]d.[–2, ∞)e.None of these

To find the domain of f-1, we need to consider the range of the original function f(x) = –√(x – 5) – 2.

First, let's determine the domain of f(x). The square root function is defined for non-negative values, so we need to find the values of x for which (x - 5) is greater than or equal to 0.

Setting (x - 5) ≥ 0, we solve for x: x ≥ 5

Therefore, the domain of f(x) is x ≥ 5.

Now, to find the domain of f-1, we need to consider the range of f(x). The range of f(x) is the set of all possible output values. Since the square root function is always non-negative, the range of f(x) is f(x) ≥ 0.

To find the domain of f-1, we need to determine the values of x for which f(x) ≥ 0.

Substituting f(x) = 0 into the original function, we have: –√(x – 5) – 2 = 0

Solving for x, we get: –√(x – 5) = 2 √(x – 5) = -2

Since the square root of a number is always non-negative, there are no values of x that satisfy this equation. Therefore, the range of f(x) does not include 0, and the domain of f-1 is None of these (e).