The Day I Knew...

Today is the day I knew, beyond a shadow of a doubt, that my decision to finally outsource my son's math instruction this year was a good one. This is the letter to his teacher--written totally "in Greek"--which I found cc'ed in my inbox today:

Mrs. M.,
When we find the inverse of a function and then prove that f(f-1(x)) = x and f-1(f(x)) = x, does that mean that f(x) = f-1(x)?
If we solve for f(x) = f-1(x), though, they don't cancel each other out. For instance:


f(x) = 6x

f-1(x) = x/6

If f(x) = f-1(x), then 6x = x/6, which is impossible, because then:

6x = x/6
x = x/36
1 = x/36x
1 = 1/36

OR

x/6 = 6x
x = 36x
1 = 36x/x
1 = 36

But, since f(f-1(x)) = x is true, f-1(f(x)) = x is true, and f(x) ≠ f-1(x) is true, does that mean that x ≠ x? I'm a little confused by this... Could you explain it for me?

Thanks,
PT

Hunh?! Thankfully, he is now asking somebody besides me!!

Fed Your Brain Today?

In this gloriously packed time of adjusting to a new homeschool schedule, I have run across this wonderful link to a great site.



I'm putting a permanent link in the sidebar so my kids can easily find it.  Thanks to Ann Voskamp and her wonderful blog for this list!  (This link will lead you to her blog post.  Scroll down past the photos to get to the list.)