Question

Please Help!. Consider the function. f (x) = 1/2x +1. a. Find the inverse of f(x) and name it g(x). Show and explain your work. . b. Use function composition to show that f(x) and g(x) are inverses of each other. . c. Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.

Answer 1

The inverse of a function is determined by substituting f(x) by y and expressing the function in terms of x = ... Then exchange the places of x and y. In this problem, y = 0.5 x -1; x = 2(y+1) . Then g(x) = y = 2x +2. The graphs are linear but g(x) has a larger slope compared to f(x).