f(x)=2x+1. Draw y=f(x), y=f^1(x) and y=x on the same axes.

Question

f(x)=2x+1

 

a. was to find f^1(x) inverse, which I got (y-1)/2

 

b. Draw y=f(x), y=f^1(x) and y=x on the same axes.  There is a graph paper provided for the question.

Answer 1

To find the inverse of y = 2x + 1,

 

first SWITCH x and y:

 

  x = 2y + 1

 

 

Now you solve for y

 

x-1 = 2y

 

(x-1)/2 = y

 

So your inverse is correct, you just forgot to switch x and y

 

When you graph them on the same plot, you will see the identity line y=x split them down the middle;

You can go to www.desmos.com to get a good graph of most any function

 

Finally to check:

  

   f comp f-inverse

  2( x-1)/2 + 1 = x-1 + 1 = x

 

and 

 

 f-inverse comp f

 [(2x+1)-1]/2 = 2x/2 = x