Embed Size (px)
DESCRIPTION
Citation preview
3.512th feb 2013
1
February 12, 2013
Feb 1212:45 PM
3.512th feb 2013
2
February 12, 2013
Mar 11:56 PM
Let's practice writing inverse equations. Notice that functionsmight have inverses that are NOT functions.
3.512th feb 2013
3
February 12, 2013
Mar 12:00 PM
3.512th feb 2013
4
February 12, 2013
Mar 11:56 PM
If we wish to use the symbol f1(x) we usually mean the inverse FUNCTION.But we cannot use the word function if the inversehas an x value that produces more than one y value.
We can easily tell if a function's inverse is also a functionby using the HORIZONTAL line test.
Ex) Look at the graph of f(x)=x2 and the graph of f(x)=Would their inverses also be functions.
In this case, since the root of x only exists for positive x values (or zero), then its inverse is NOT all of x2, but only the domain where x is greater than or equal to 0.
Find theinverse equation.
Find theinverse equation
3.512th feb 2013
5
February 12, 2013
Mar 12:17 PM
Do these functions have inverses that are also valid functions?
3.512th feb 2013
6
February 12, 2013
Mar 11:46 PM
In the example, notice that the algebra to producethe inverse resulted in the function . The domain of f(x) was greater than or equal to 0, but we had to RESTRICTthe Domain or the inverse function.
We can use this same concept in our original functions so that the inverse is still a FUNCTION.By restricting part of the domain, we can produce a functionthat passes both the VERTICAL and the HORIZONTAL linetest. This will ensure that the inverse is a function with one xvalue producing one y value.
Ex) Graph f(x) =x2 where x>0.Now solve for f1(x) and draw its graph.Notice by restricting the domain, f(x) passes the VLT and HLT.Notice that f1(x) passes the VLT which means it is a function.
3.512th feb 2013
7
February 12, 2013
Mar 12:40 PM
3.512th feb 2013
8
February 12, 2013
Mar 13:05 PM
3.512th feb 2013
9
February 12, 2013
Mar 12:48 PM
3.512th feb 2013
10
February 12, 2013
Mar 13:06 PM
What would happen at the intersection point of afunction and its inverse.
Find the inverse of f(x)=2x4.
How would we algebraically solve for their intersection??
What do we notice?? Why does this make sense??
3.512th feb 2013
11
February 12, 2013
Mar 13:09 PM
Homework; Page 243#410a,11,12, 13 (Challenge!)Mult. Ch. #1,2
Do #7a)c) and #11 in class.
![BOYMOR.QLE QL.REP] - Stacksxk898wv6983/xk898wv6983.pdf · 15 jun 1978 6:55 boymor.qle ql,rep] page 1-1 (cont.) (cont.) (cont.) (cont.) (cont.) (cont.) prover prover (cont.) 5 comment](https://img.pdfslide.us/doc/110x75/6057337242a55f07515b3baa/qlrep-stacks-xk898wv6983xk898wv6983pdf-15-jun-1978-655-boymorqle-qlrep.jpg)
