Yes, one-to-one function and its inverse are equal.

This must be true, when the graph of function  and the graph of function  symmetric about the line .

Consider the function .

Rewrite the above function as .

To find inverse interchange the variables and .

Solve for .

.

Inverse of the function is . 

Graph :

Graph the functions and .

Observe the graph and symmetric about the line .

Thus, one-to-one function and its inverse are equal.

 Yes, one-to-one function and its inverse are equal.