inverse function

Question

Give two different examples of functions that are equivalent to their inverses. show how you know 

Answer 1

Take for example:

f(x) = 2-x

 

Step 1:  replace f(x) with y

 

y = 2 - x

 

Step 2: switch x and y in the equation

 

x = 2 - y

 

Step 3: solve for y

 

x-2 = -y

-x+2 = y

y = 2 - x

 

Step 4: Replace y with f^-1(x)

 

f^-1(x) = 2-x

 

As you can see, f(x) and the inverse f^-1(x) are the same

 

 

Another very simple example would be the function

f(x) = x   or   y = x

Answer 2

For a function to equal its inverse, we must have f(f(x)) = x.  I'll give you one example:

 

f(x) = 1/x

 

If we evaluate f(f(x)), we get

 

f(f(x)) = f(1/x) = 1/(1/x) = x

 

Of course, this function is undefined at zero, but hopefully, that gives you enough of an idea to think of a few more.