Inverse Functions . End In Mind. Prove that and are inverses of each other Complete warm up individually and then compare to a neighbor. Vocabulary . Function: a relation in which each input x has exactly 1 output y
Can you mentally determine the inverse of the functions?
Finding the inverse of a function
Example: f(x)= 3x-8 and g(x) = x2+1
substitute the g(x) function
for the f(x) function
f(g(x))=f○g(x) = 3(x2+1)-8
To verify that two functions are inverses then,
Using our earlier problem,
Verify that and are inverses of each other.
The graph of the inverse of f is the reflection of f over the line y=x
a function f has an inverse function if and only if the function is one to one.
a function f is one to one if for every y there is exactly one x value
Not invertible. Since 2 y values are the same.
Not invertible since all y values are the same.
End in Mind: limit the domain so that the inverse is a function
Is the relation a function?
Graph the function.
Does the inverse exist?
How could you limit the domain so that the function will have an inverse?
Graph the inverse with the restricted domain. How can you verify that the graph of the inverse exits?
GO to the above website for further explanations. You must do the practice problems. Each problem will tell you if you are right or wrong. If you need help, click the explanation button