Lecture 8: Composition of Functions

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By today you should have read through section 2.3 of the text and done problems 25 and 51 in section 2.3.

Brief review of the lecture

We constructed the function V(x)=x(11-2x)(8.5-2x) which describes the volume of a box obtained by cutting x by x squares from the four corners of an 8.5 by 11 sheet of cardboard, and bending up the flaps. Later, we'll see how to maximize this function.
Then we discussed composition of functions. We worked the following problems:
Let f(x)=x2+1, and g(x)=(x-2)(1/2).
Find representations of the composite functions fog and gof.
Solution fog(x)=x-1 and gof(x)=(x2-1)(1/2).
We also noted the very important fact that although (sqrt x)2=x, it is NOT true in general that sqrt(x2)=x. Try x=-1, and see.
We then discussed piecewise defined functins and how they compose with other functions. f(x) = 2x +1 if x is less than 1 and =3x if x is at least 1. Compose this with g(x)=x2-2 in both ways.

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