Question

f(x) = 2x + 5, A. Graph the functions f(x) and g(x) on the same coordinate plane. You may use technology to create the graph of the functions or submit a handwritten graph. B. In two or more complete sentences, explain how to use the graphs of f(x) and g(x) to prove that the functions are inverses of each other.

Answer 1

we have

$f(x) = 2x + 5\ g(x)=(x-5)/2$

we know that

The graphs of inverse functions are a reflection over the line y = x.  If you can see from the graphs that one is a reflection of the other over the line y = x, then that proves they are inverse functions

using a graph tool

see the attached figure------> you can see from the graph that one is a reflection of the other over the line y = x

therefore

the functions f(x) and g(x)  are inverse functions

the answer is

Part a) see the attached figure

Part b) see the explanation above