6 7 Inverse Relations and Functions Using a

6. 7 Inverse Relations and Functions

Using a graphing calculator, graph the pairs of equations on the same graph. Sketch your results. Be sure to use the negative sign, not the subtraction key. What do you notice about the graphs? These graphs are said to be inverses of each other.

An inverse relation “undoes” the relation and switches the x and y coordinates. § In other words, if the relation has coordinates (a, b), the inverse has coordinates of (b, a) Function f(x) X Inverse of Function f(x) Y X Y 0 3 3 0 1 4 4 1 -3 0 0 -3 -5 2 2 -5 2 5 5 2 -8 5 5 -8

Let’s look at our graphs from earlier. Notice that the points of the graphs are reflected across a specific line. What is the equation of the line of reflection? y=x

Finding the Inverse of an equation Find the inverse of y=x 2+3 x=y 2+3 Switch the x and y x – 3 = y 2 Solve for y Find the square root of both sides

What happens if I don’t include the + ? § Graphing the function and only the positive graph of the inverse. . . We only get half of the inverse graph.

Finding the Inverse of a we find the inverse of a function When function f(x) we write it as f -1 Find the inverse of Rewrite using y Switch the x and y Square both sides Solve for y

Let’s Try Some Find the inverse of each

Composition of Inverse Functions For the function