Example 1. Let 
(Assume the function is one-to-one function.) Find f-1(x). First
we set 
and solve for x.
We see 
and raise the exponents
to 4 both sides yields, 
Finally, we write 
for 
(The reason we restrict 
is to make f-1 a
one-to one function, otherwise f-1 will not have an inverse.) Let's
verify this inverse by following two methods.
Method 1. (Checking f(g(x))=g(f(x))=x).
You could use the following Maple commands to check your answer:
f:=x -> 2*x^(1/4);
g:=x -> (x/2)^4;
simplify(f(g(x)));
simplify(g(f(x)));
Method 2. Check if the graphs are symmetric to y=x.
f:= x -> 2*x^(1/4);
g:=x -> (x/2)^4;
plot({f(x),g(x),x},x=0..10,y=0..10, scaling=constrained);
You should get something like this .
Example 2. Let 
for 
This function is one-to-one
function if 
why?). Find f-1(x).
First we set 
and solve for x.
Take the square root both sides, yieds, 
Finaly, we write 
Can you use two methods mentioned above to
verify indeed f-1 is the inverse of f?
