Inverse Relation: The set of ordered pairs obtained by
exchanging the x-coordinates with the y-coordinates in a
relation.
Example: Find the inverse of the relation
x
x
y
4 -5
2 3
-3 6
inverse
Patty Paper Activity...
x
x
y
4 -5
2 3
-3 6
inverse
y
y
Every function has an inverse function
The inverse of f(x) is written
-1
f (x)
We say: "f of x inverse"
or
"the inverse of f of x"
To find the inverse of a function:
Step 1: Replace f(x) with y in the equation for f(x)
f(x) = 4x - 8
Step 2: Interchange y and x in the equation
Step 3: Solve the equation for y
Step 4: Replace y with f -1(x) in the new equation
Find the inverse of the function:
f(x) = 2x + 6
Now graph on patty paper...
Find the inverse of the function:
f(x) = -1 x + 11
2
Find the inverse of the function:
3y + 24 = 2x
Sam rents a car for a day.
The total cost C(x) in dollars is given by
C(x) = 19.99 + 0.3x
where x is the number of miles he drives.
-1
Find the inverse function C (x)
What do x and C-1 (x) represent in the context of the
inverse function?
How many miles did Sam drive if his total cost was $34.99?
Write an equation for the inverse function f -1(x) that
satisfies the given conditions
slope of f(x) is 7, graph of f -1(x) contains the point (13,1)