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Here is a graph of a function g which looks as if it has an inverse. Since you can't see the whole graph, just assume that g does have an inverse. Suppose the inverse function is named f. You can see the graph of f in its usual configuration by looking at the graph of g through the back of the screen.
Next to the graph of g is the same graph, with a tangent line added. If you look through the back of the screen, you can see the graph of f with a tangent line added.
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1. If the tangent line to the graph of g has slope 2, what is the slope of the tangent line to the graph of f?
2. If you know that g(3) = 5, what do you know about f?
3. If you know that g(3) = 5 and g'(3) = 2, what do you know about f'?
4. If you know that g(3) = 5 and g'(3) = 2, what would you estimate g(3.02) is?
5. If you know that g(3) = 5 and g'(3) = 2, what would you estimate f(5.03) is?
6. If you know that H and K are functions which are inverses to one another and you know that H(a) = b and that H'(a) = c, what conclusions can you draw about K and K' ?