There seems to be a problem with the pop-up announcements on iCollege. Thus, I will accept today’s homework on Thursday.
Test 2 is on Thursday, 1 October 2009 and will cover finding domains, even/odd functions (Section 1.4), Section 1.6 and Section 1.7.Today, we covered several examples of finding inverse functions. There are several ideas that you must make sure that you carefully consider when finding an inverse function:
1. f(x) must be 1-to-1 in order to be able to find the inverse. So, in step 1, you need to determine if f(x) is 1-to-1. To determine if f(x) is 1-to-1, graph and use the horizontal line test. If the function is not 1-to-1, then you must restrict the domain of f(x) so that if will have an inverse.
2. Check your answer. There are two ways to check: i. finding both f(f –1(x)) and f –1(f(x)) and checking that they both are equal to x; ii. graphing f(x), f –1(x) and y = x and checking that the graphs of f(x) and f –1(x) are mirror images over the y = x line. It is possible that you need to restrict the domain of f –1(x) to ensure the graphs of f(x) and f –1(x) are mirror images.
3. To graph a function with a restricted domain use the same idea that we used for piecewise-defined functions. For example, if we wanted to graph f(x) = x2 – 6x + 9, x ≥ 3, then enter y1=(x^2-6x+9)(x≥3) into the TI83/84 and graph. To find the inequalities press 2nd key, then math key.
The next homework is due on Thursday, 8 October 2009 and will consist of the following:
Section 1.7: # 59, 62, 63, 66, 68, 69, 71, 74, 75
