Sept. 12 Class

Learning Goal: Understand how to find the inverse of a function.

Today we discussed what the inverse of a function means:

If a function takes an x as input and gives a y as output, then the inverse works in the opposite direction, taking the y as input and gives an x as output.

For an inverse the domain and range is reversed compared to the original function.

For a function, , the inverse is denoted .


Example: For the function f(x) = {(1, 2), (3, 2), (4, 5)}, what is the inverse?

Solution: The inverse is found by switching the x and y values,

Notice that this inverse is not a function, even though the original was a function!

The inverse of a function is not always a function.

Example: Find the inverse of f(x) = 3x – 5.

Solution: Follow these steps to find the inverse of an equation,

Example: Find the inverse of this graph.

Solution: You can take each point (x,y) and switch it, then plot the solution, 

OR 

you can reflect the graph over the diagonal line y = x.

Either way, you get this result:

There will be a formative quiz on the material so far this Friday.

Homework

Pg. 46 #1-7(eoo), 9-17