2. consider the function . a.) find the inverse of f(x) and name it g(x). show and explain your work. b.) use 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 what about your graph shows that the functions are inverses of each other. first correct answer will get 25 pts and so ! : d

Part A:

Given that , we find the inverse g(x) as follows:

First, we rewrite the function as:

Next, we switch x and y and then solve for y as follows:



We then rewrite the equation using function notation to get:



Part B:

For two function that are inverse of each other, the composition of the two functions gives x.

Thus,



Since, f o g = g o f = x, hence g(x) is the inverse of f(x).

Part C:

The graphs of f(x) and g(x) are attached.

From the graph it can be seen that the prperties of both graphs are similar, the properties of one graph in the x-axis correspond to the properties of the other graph in the y-axis and vice-versa. Also, the two lines intersect at a point were x = y.