Precalc Warm Up #
f(x) =
9-3
Homework Quiz First!
g(x) = 2x - 5
Find (if it exists) and state the domain and range
1.
f(g(x))
2.
(f f)x
3. (g g)x
Questions on #9-2 ?
2
f(x) = x + 1
g(x) = x - 3
1. Find g(f(7))
2
f(x) = x + 1
2. Find g(f(4))
3. Find g(f(x))
g(x) = x - 3
f(x) =
2x
-1
_______
g(x) =
5
1. Find f(g(3))
2. Find f(g(-1))
3. Find f(g(x))
5x
+1
_______
2
f(x) =
g(x) =
5x
+1
_______
2
2x
-1
_______
5
Inverse functions
We have looked at composite functions. Can you find
g(x) so that when f(x) = 2x + 3
g(f(x)) = x ???
In other words, g(x) undoes f(x), because if
x was your input and now it is your output, you've done
x
nothing at all!
2x + 3
???
x
We say g(x) is the inverse of f(x) since f(g(x)) = g(f(x)) = x
Find f -1 for the following. State domain and range for
function and inverse.
1. f(x) = 4x - 5
2.
3.
4. f(x) = 2x3 - 1
5.
How are the graphs of two inverse function related?
Graph f(x) = 4x -8
dom:
range:
f-1(x) =
dom:
range:
and it's inverse on the same axis
Graph
and it's inverse on the same axis
dom:
range:
f-1(x)=
dom:
range:
Not all functions have inverses that are also functions.
For example,
f(x) = x2
has no inverse function. In order for a function to have
an inverse function, the original function must be one to
one. Which of the following functions have inverse
functions?
1. f(x) = x3 +1
2. g(x) = x2 - x
3. h(x) = √x
For the inverse function of f
(called f -1)
to exist, then
1. f must be a one to one function
2. The domain of f is the range of f -1. The range of f
is the domain of f -1
If the above holds true, and f(f -1(x)) = f -1(f(x)) = x ,
then f(x) and f -1(x) are inverses of each other.
How do we find the inverse function of another function?
step 1: Check that your function is one to one. If it is not,
the inverse will exist, but not as a function.
step 2: Find the domain and range of your function.
Switch them and set them as your domain and range for
your inverse.
step 3: In your equation, swap x for y. Then solve for y.
This is your inverse!
Find the inverse function of
graph both functions.
and
Find the inverse function of f(x)= x2+4x , x < -2
State dom and range and graph both
Can you think of any function that is it's own inverse?
y=x
Find the inverse of
,
x>1
#9-3 SL book
p. 164 1 LC , 3, 5abcd, 9 ,10, 11 12