Question

1. Find the inverse of the function g, denoted as g^(-1), and then calculate g^(-1)(-1).

2. Find the inverse of the function h, denoted as h^(-1), and express it in terms of x.
3. Calculate (h ∘ h^(-1))(4), where (h ∘ h^(-1)) represents the composition of the function h with its inverse h^(-1).

You can use these questions to work through the given functions and find the requested values.

Answer 1

To find the inverse of a function, swap x and y and solve for y. To calculate the composition of a function and its inverse, substitute the value into the inverse function and then into the original function.

Step-by-step explanation:

To find the inverse of a function, you need to swap the roles of x and y and solve for y. For example, if the original function is g(x), the inverse function is denoted as g^(-1)(x). To calculate g^(-1)(-1), you substitute -1 for x in the inverse function and simplify the expression to find the corresponding value of y.

To find the inverse of a function h and express it in terms of x, you can follow the same process of swapping x and y and solving for y.

To calculate (h ∘ h^(-1))(4), which represents the composition of the function h with its inverse h^(-1), you substitute 4 for x in h^(-1) and then substitute the resulting value into the original function h.