Transcript P-4 Inverse Functions

1.6 Inverse Functions
Review of things we already know
One to One Function:
f(a)  f(b) if a  b
That is, while a function specifies that every
x has a unique y, a one to one function
specifies that ALSO every y has a unique x.
The horizontal line test
An Inverse Function
f 1 (x) is the inverse of f(x) if
f f
1
 x and f
1
f x
How to find an inverse? Switch x and y and
solve for y.
Graph of an Inverse
f(x)
(1,2)
f-1(x)
(2,1)
Logarithms
“logarithm” is the term for the inverse of any
exponential function.
y = 2x  The inverse would be x = 2y
This is written officially as log2x = y
How to look at logarithms
logbx = y can be thought of as logbn = p
Then rewrite as n = bp
(notice the significance of
the variables chosen!!)
And then solve it!
Some Rules
1.
If logbx1 = logbx2 then x1 = x2
2. Logbb = 1
3. logb1 = 0
4. logbbx = x
5. lnex = x
6. blogbx = x
7. elnx = x
8. bx = exlnb
There are 4 Laws of Simplification
1. log b M  log b N  log b MN
M
2. log b M  log b N  log b
N
p
3. log b M  plog b M
log c M
4. log b M 
log c b
Get out that graphing calculator!!
Lets graph two functions and find their point
of intersection.
y = 3x and y = x3