f(x)=(1/3)x–4 on the interval [2,9]. The domain of the inverse function is the interval [A,B]

where A=? and B=?

y(2) = -10/3

y(9) = -1

so, A = -10/3 B=-1

To find the domain of the inverse function, we need to determine the range of the original function f(x).

Given that f(x) = (1/3)x - 4, the domain of f(x) is the interval [2, 9].

To find the range of f(x), we can calculate the minimum and maximum values that f(x) can take within the given interval.

Let's start by evaluating f(x) at the endpoints of the interval:
f(2) = (1/3)(2) - 4 = (2/3) - 4 = -3 1/3
f(9) = (1/3)(9) - 4 = 3 - 4 = -1

So, within the interval [2,9], the range of f(x) is [-3 1/3, -1].

To find the domain of the inverse function, we interchange the roles of x and f(x) and solve for x.

Let y = f(x)

Original function: y = (1/3)x - 4

Interchanging x and y: x = (1/3)y - 4

Now, let's solve this equation for y:

x + 4 = (1/3)y

Multiplying both sides by 3:

3(x + 4) = y
3x + 12 = y

Therefore, the inverse function is y = 3x + 12.

To find the domain of the inverse function, we need to determine the range of this inverse function.

For the inverse function y = 3x + 12, there are no restrictions on the values x can take. Hence, the domain of the inverse function is the set of all real numbers.

Therefore, the domain of the inverse function is the interval (-∞, +∞).