Question

Show that f and g are inverse functions (a) analytically and (b) graphically.

f (x) = x^3,                      g (x) = ∛x

Answer 1

Step 1:

The functions are and

A function is the inverse of the function if  for each in the domain of .

and for each in the domain of .

        

       

         .

Step 2:

          

        

          .

Since , the functions and are inverse functions.

Answer 2

Contd...

Step 3:

Graph the two functions.

Choose random values for and find the corresponding values for .

 

 

Comments

 Contd..

Step 4:

Graph:

Draw the coordinate plane.

Plot the points of and connect the curve.

Plot the points of and connect the curve.

Observe the graph: and have reflective property.

Solution:

and are inverse functions.