Answer: The inverse of a function is found by switching the positions of the input and output values in the function. For example, if the function is f(x) = 2x, the inverse would be f<sup>-1</sup>(x) = x/2.
In the case of the given function, f(x) = 8√ x, the inverse can be found by switching the positions of the input and output values. This gives us f<sup>-1</sup>(x) = √ x/8. This means that if x is the input value, the output value will be √ x/8. Note that the domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function. In this case, the domain of f<sup>-1</sup>(x) is [0, ∞) and the range is [0, ∞), since these are the range and domain of the original function.
Here is the complete inverse function:
f<sup>-1</sup>(x) = √ x/8 for x > 0.