a function and its inverse are shown on the same graph. complete the sentences to compare the functions. the…

a function and its inverse are shown on the same graph. complete the sentences to compare the functions. the range of f⁻¹(x) is the domain of f(x) is the minimum of f(x) is equal to the

a function and its inverse are shown on the same graph. complete the sentences to compare the functions. the range of f⁻¹(x) is the domain of f(x) is the minimum of f(x) is equal to the

Answer

Explanation:

Step1: Recall property of function - inverse

The range of the inverse function (f^{-1}(x)) is the domain of the original function (f(x)).

Step2: Recall another property

The domain of (f(x)) is the range of (f^{-1}(x)). Also, the minimum of (f(x)) is equal to the minimum - value of the (y) - coordinates of (f(x)) and this is equal to the (x) - coordinate of the point on (f^{-1}(x)) where (f^{-1}(x)) has a horizontal tangent (due to the symmetry of a function and its inverse about the line (y = x)). In terms of domain - range relationship, the minimum of (f(x)) is equal to the (x) - value of the point on (f^{-1}(x)) corresponding to the minimum (y) - value of (f(x)), which is the maximum of the (x) - values for which (f^{-1}(x)) is defined in the relevant part of the graph. The minimum of (f(x)) is equal to the maximum of the domain of (f^{-1}(x)).

Answer:

The range of (f^{-1}(x)) is the domain of (f(x)); The domain of (f(x)) is the range of (f^{-1}(x)); The minimum of (f(x)) is equal to the maximum of the domain of (f^{-1}(x))