PRE-CALCULUS/TRIG 3
Name:_________________________________
1.9 Inverse Functions
Inverse function:
________
Notation: Inverse of f(x) = ________
 Inverse functions are _______________ (when each ‘y’ (output) corresponds to only one ‘x’ (input) value)
Note: If the function is One-to-One, then ___________________________________.

f(x) = {(1,3), (3,5), (5, 7)}

f-1(x) = { (
1) Show that f(x) =
x6
2) Determine if f(x) =
3
x-2
3
,
), (
,
), (
,
)}
and g(x) = 3x – 6 are inverse functions.
and g(x) = 3x – 2 are inverses of each other.
Steps to determine inverses (informally):
1) _____________________ f(x) with y
2) **______________ the x and the y
3) Solve for y
1
4) **Replace y with f ( x)  inverse notation
Find the inverse of the following functions. Then state whether the inverses are functions.
3)
(a)
f(x) = x2 + 2
(b)
f(x) = (x + 2)3 – 3
4) Find the inverse of f(x)= x2 – 4. Then graph both the function and its inverse on the same graph.
Parent:
x
Parent:
y
x
Vertex: (_______)
y
Vertex: (_______)
**Graphs of inverses are ______________ about the line ________**
How would we tell if the inverse is also a function?
General rule for polynomial functions,
_______________________________
(“n” is the ________________________________)
 If n is even, the inverse of f(x) = xn is not a function
 If n is odd, the inverse of f(x) = xn is a function.
Is the inverse a function?
y = (x – 1)3 + 1
___________
y = 4(x + 1)2 – 2
____________
PRACTICE:
Determine if the given functions are inverses of each other. Write yes or no. Show your work!
1.
f(x) = 3x – 5
2.
f(x) = x – 10
__________
g(x) =
3. f(x) =
__________
x5
3
g(x) = x + 10
2x  3
5
4.
f(x) = 3x – 7
__________
g(x) =
3x  5
3
__________
g(x) =
1
x+7
3
Find the inverse of each function. Then state whether the inverse is a function.
5.
f(x) =
x5 + 1
f(x) =
6.
inverse: __________
inverse: __________
function?:__________
function?:__________