You should KNOW

1. What a one-to-one function is and how to recognize graphically if a function is one-to-one

2. What an inverse of a function is, namely, that g is an inverse for f if f(g(x))= x and g(f(x)) =x. (This is the definition in JIT p. 147 and FP p. 93, and the one you should learn.) Thus, when f and g are inverses, each function "undoes" the other one and we write g = f^{-1}

3. That one-to-one functions have inverses, but functions that are not one-to-one don't (unless we restrict their domains).

4. How the graphs of a function and its inverse are related, namely, that they are reflections of each other around the diagonal in the plane.

You should be ABLE TO

1. Determine algebraically and/or graphically if a function is one-to-one.

2. Find inverses of simple functions by non-algebraic reasoning using the idea that the inverse undoes the function.

3. Find inverses algebraically using the "switch and solve" method and express your results using proper conventional notation.

4. Sketch a graph of the inverse of a function using general principles.

5. Verify that two functions are inverse to each other by looking at their compositions.