To me, they're some of the most straight-forward multiple choice questions the students encounter on the exam; yet, year after year they miss this question (at least on their unit tests and mock exam).
So, clearly, not as straight-forward as I thought...
This year I formalized a strategy for them in three steps. Not all three of these steps are necessary every time; but, if my students took the time to follow all three steps, they got these questions correct.
Here are the steps:
If f and g are differentiable functions and g is the inverse of f, then to find g'(a):
- List all points given on f as ordered pairs.
- List the points you now know are on g (switch x and y).
- Follow this formula: g'(a)=1/(f'(g(a)).
Following the steps, we would work this question as follows:
How about one that describes f as an algebraic or numeric function, such as this FRQ from 2007:
Students could certainly start with Step 1 again and work their way down, but I encourage them--once they get comfortable--to feel free to start with Step 2 and fill in the blanks as they see fit. Here's how I would suggest they work this problem: