What does this student know about composition of functions?

What’s going through the kid’s brain when he makes his mistake?

How would you help?

- Post author By mpershan
- Post date August 8, 2012
- 4 Comments on Keeping your composure (? does that even count as a pun?)

## 4 replies on “Keeping your composure (? does that even count as a pun?)”

I think we saw this one before – originally I thought the -1 was an arrow. – 1 – 7 is 6 because two negatives make a positive. My guess is that this student is trying to distribute instead of compose, but can’t do that either. This is somewhat typical for students that have had a huge amount of “help” to allow them to pass in mainstream classes – very tough to find a productive way to proceed.

Oops! I’ll post a new one and get rid of this post. Want me to move your comment to the original?

I think the somewhat ambiguous ‘->’ is an arrow. The misconception is substituting x into a function already defined in terms of x, giving the student the erroneous x^2. Then they draw an arrow because they perhaps haven’t been shown how to correctly connect intermediate steps leading to their final answer. I would give them the benefit of the doubt for correctly adding 7.

Just noticed the power of x increased again. More of the same initial problem? I’m sure the student would unpick their mistake if they were asked to think about substituting say x=3 into their final result.