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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Product and Quotient of Functions

We may also evaluate the product or quotient of two functions by another method. That is, we first evaluate each function, and then we multiply or divide.

Example 1

Given f(x) = x2 - 13 and g(x) = x + 9, find (f Â· g)(x) when x = -4. That is, find (f Â· g)(-4).

Solution

 Step 1 Use x = -4 to find f(-4) and g(-4). Substitute -4 for x in f(x). Simplify. So, f(-4) = 3. Substitute -4 for x in g(x). Simplify. So, g(-4) = 5. f(-4)     g(-4) = (-4)2 - 13 = 3   = (-4) + 9 = 5 Step 2 Find f(-4) Â· g(-4). Multiply. f(-4) Â· g(-4) = 3 Â· 58

So, (f Â· g)(-4) = 15.

Example 2

Given f(x) = 3x2 - 8 and g(x) = x + 19, find when x = 6. That is, find

Solution

 Step 1 Use x = 6 to find f(6) and g(6).Substitute 6 for x in f(x). Simplify. So, f(6) = 100. Substitute 6 for x in g(x). Add. So, g(6) = 25. f(6)     g(6) = 3(6)2 - 8 = 100   = (6) + 19 = 25 Step 2 Find Divide. = 4

So,

Note:

This method is preferred by many students for evaluating the sum, difference, product, or quotient of two functions. This is because numbers are substituted immediately and so the calculations are often easier.