Transcript Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.

Ch 9 – Properties and Attributes of
Functions
9.5 – Functions and their Inverses
What is the inverse of a
function?
 The inverse of a function f(x) “undoes” f(x)
 Its graph is a reflection of f(x) across the line
y=x
 Sometimes, the inverse ends up NOT being a
function.
 If the inverse is a function, then it is denoted
as f-1(x)
Horizontal-Line Test
If any horizontal line passes through more than one point
on the graph of a relation, the inverse relation is NOT a
function.
The inverse relation
is a function
The inverse relation
is not a function
Use the horizontal-line test to determine
whether the inverse of each relation is a
function.
Finding Inverses of functions
 To find the inverse
 Example: Find the
of a function, switch
inverse of f(x) = x2
the x and y, then
solve for y.
Find the inverse f-1(x) of f x  3 x 1.
Determine whether it is a function, and
state its domain and range.
When both a relation and its inverse are
functions, the relation is called a one-toone function.
 In a one-to-one
function, each
y-value is paired
with EXACTLY
one x-value.
 You can use
composition of
functions to verify that
two functions are
inverses.
 If f(g(x)) = g(f(x)) = x
then f(x) and g(x) are
inverse functions.
Determine by composition whether
each pair of functions are inverses.
A.
f x   3x  1
1
g x   x  1
3
B. For x  1 or 0,
1
f x  
x 1
1
g x    1
x