I have a graph of a one-to-one function. I need to Draw the graph of the inverse function, f^-1

please help. not calculus

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Every function is a relation, or a set of ordered pairs (x,y). Every relation has an inverse relation where you exchange x and y. (For every (x,y) in the relation, the inverse relation has the point (y,x)).

If the function is one-to-one, then its inverse relation is also a function.

Given the graph of a one-to-one function, to graph its inverse you just take each point on the graph `(x_i,y_i)` and plot `(y_i,x_i)` . e.g., if (1,2) is on the function, then (2,1) will be on its inverse.

If done correctly, you will notice that the graph of a function and its inverse are symmetric across the line y=x, or the line y=x is a line of symmetry. Every point on the function has a mirror point across the line y=x on the inverse.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial