Consider the function f(x)=−x2+6 on the domain [0,∞). Use the range of f(x) to determine the domain of f−1(x). What is the domain of f−1(x)?

Question

OPTIONS:

−6<x<6

−∞<x≤6

6<f−1(x)<∞

−∞<f−1(x)≤6

6<x<∞

−6<f−1(x)<6

Answer 1

The range of f(x) is the domain of f^-1(x).

The graph of y = f(x) is the right half of a parabola opening downward with highest point at (0,6).

So, the range of f(x) is (-∞, 6].

Thus, the domain of f^-1(x) is (-∞,6]

Range of f^-1(x) = Domain of f(x) = [0, ∞)