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