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The topic along with functions which we ought to deal with is combining functions. For the most part this means performing fundamental arithmetic (subtraction, addition, multiplication, & division) with functions. There is one new means of combing functions which we'll need to look at as well.
Let's begin with basic arithmetic of functions. Given two functions f(x) & g(x) we have the following notation & operations.
( f + g )( x) =f ( x ) + g ( x ) ( f - g )( x ) =f ( x ) - g ( x )
( fg ) ( x ) = f ( x ) g ( x ) (f /g) ( x ) = f ( x )/ g ( x )
Sometimes we will drop the ( x )part & just write down the following,
f + g = f ( x ) + g ( x ) f - g=f ( x ) - g ( x )
fg =f ( x ) g ( x ) f/g = f ( x ) /g ( x )
Note as well that we put x's in the parenthesis, however we will frequently put in numbers as well.
Using transformation sketch the graph of each of the following. g ( x ) = - x 2 Solution (a) Depending on the placement of
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Simpler method Let's begin by looking at the simpler method. This method will employ the following fact about exponential functions. If b x = b y then x
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Carl and his dad I stonecarvers. Carl can cut the stone in five days. With his father''s help he can carve it in two days. How long would take his father to carve it alone. Bob c
Methods for solving systems We will be looking at two methods for solving systems in this section. Method of substitution The first method is known as the method of sub
si el log de 28 en base 14 es a cuanto es el log de 16 en base 49
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