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:

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ReplyDeleteOpposite capacities are imperative in Mathematics and also in numerous connected territories of science. The most celebrated combine of capacities backwards to each other are the logarithmic and the exponential capacities. Different capacities like the digression and arc tangent assume likewise a noteworthy part.

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