Questions about the Summer Work

Hope you're not too bogged down with the work (Well if you are waiting until the last minute: Shame on You!)

I received this email from one of you and I thought maybe some of you silent ones might have similar questions:
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> Hey Mr. Lemay,
> Just wonder how to do the following problems:
> 16-22 even, 36, 38, 39, 60,61, 63, and 67.
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My reply:

Dear STu Dent:

For 16 - 22:

I've given you the 4 function definitions. What these questions are asking you to do is to find the values of the these "composite functions"

For example if f(x) = 2x-1 and g(x) = the points {(1, 2), (2, 3), (3, 4)}

find (f+g)(2)

This means find f(2) = 2(2)-1 or 3 and g(2) = 3 and add the two numbers together.

OK?

36, 38, and 39 are just exponent properties. A good review/explanation can be found here:

http://www.purplemath.com/modules/exponent.htm

For 60 and 61. Points of intersection can be found by setting the two functions equal and solving for x and then back substituting for y.

Here is good explanation for 60 (a non-linear system)

http://www.purplemath.com/modules/syseqgen3.htm

For 61, try a graphing calculator only I want an exact answer, not a trace answer. Think about the work Mrs. B did you you around the Unit Circle and trig functions (When are Sin x and Cos x the same?)


For 63: Is 0/# = 0? Do we care about when x^3 = 0? Can we just worry about where x^4-1 = 0?

For 67: Take a look at this page: http://www.purplemath.com/modules/ineqrtnl.htm

Hope this helps. Give a yell if you need more help. I'll have you show me what you've tried.

Mr. L.