Final answer:
To verify that g(x) is the inverse of f(x), you need to show that f(g(x)) = x and g(f(x)) = x. The process generally involves finding an expression for g(x) by solving y = f(x) for x, and then swapping x and y. However, the provided function has a typo and cannot be solved as is.
Step-by-step explanation:
If f(x) = 8( ) = 5 x, to verify that g(x) is the inverse of f(x), you would need to show that f(g(x)) = x and g(f(x)) = x. One way to express this verification is by finding two expressions such that when one function is composed with the other, the result is the input variable x. Given the information provided, and recognizing potential typographical errors, we can suggest a general approach to finding the inverse of a function.
To find the inverse of the given function f(x), you would typically need to solve for x in terms of y, where y = f(x), and then switch the roles of x and y to define g(x), which should be the inverse of f(x). However, the provided function seems to contain a typo, as 8( ) = 5 x does not determine f(x) correctly. Assuming f(x) were defined properly, once you have g(x), you can verify it by checking if f(g(x)) = x and g(f(x)) = x.
As an example, if f(x) were 1/5 x, then to find its inverse, we would have y = 1/5 x, solve for x to get x = 5y, and then interchange x and y to get the inverse function g(x) = 5x. The composition of the two would give f(g(x)) = 1/5(5x) = x, confirming the inverse relationship.