Download 3.6 Inverse Functions

3.6 Inverse Functions
Inverse Relation: The result of exchanging the
input (x) & output (y) values of a function.
(That means: Flip-flop x & y, & solve for y)
f(x) = equation f-1(x) = inverse
* If the inverse is a function, it is called the
INVERSE FUNCTION.
Ex. 1 Write a table that represents the inverse of
the function given by the table.
x
g(x)
-1
4
0
3
1
4
2
1
3
5
x
g-1 (x)
Ex. 2 Find the inverse of the function.
(flip-flop x & y, & solve for y.)
f(x) = -3x2 + 5
The graph of the inverse of f is a reflection of
the graph of f across the line y = x.
One-To-One: (in a function) Every x has one and
only one y & every y has one and only one x.
So, if f(x) = function and
f-1 (x) = function, then one-to-one!!!
Horizontal Line Test: A function f is one-to-one
IFF no horizontal line intersects the graph of f
more than once. (indicates if the inverse is a
function)
Ex. 3 Determine whether the function f is
one-to-one.
a. f(x)= x4 - 4x + 3
b. f(x) = x3 + 3x - 4
If g(x) & f(x) are inverses, then:
g(f(x)) = x and f(g(x)) = x.
Ex. 4. Are the 2 functions inverses?
f(x) = x  10
g(x) = 5x - 10
5