PRE-CALCULUS/TRIG 3
Name:_________________________________ Date:_____________
Inverse function: (f ∘ g)(x) = (g ∘ f)(x) = ________
Notation: Inverse of f(x) = ________
 Inverse functions are 1-1 functions (when each ‘y’ (output) corresponds to only one ‘x’ (input) value)
Note: If the function is One-to-One, then it’s ________________ is a _____________.


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) Replace f(x) with y
2) Switch 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)
f(x) = x2 + 2
4)
f(x) = (x + 2)3 – 3
5) 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?
6)
7)
_______________________________
8)
General rule for polynomial functions,
 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?
9) y = (x – 1)3 + 1
___________
Operations with Inverses
2
Given: f(x) = 3x – 5 and g(x) = 7x – 1
11) Find (g-1 ◦ f-1)(10)
10) y = 4(x + 1)2 – 2
____________