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# Product and Quotient of Functions

We will evaluate the product and quotient of two functions for a given number. We will use the same two methods as we did for the sum and difference of two functions.

For the first example, we will use one specific method. In fact, we will first multiply the functions and then we will evaluate the product for a specific value of x.

Example 1

Given f(x) = x2 + 6 and g(x) = x2 - 5, find (f Â· g)(x) when x = 3. That is, find (f Â· g)(3).

Solution

 Step 1 Find (f Â· g)(x). Substitute for f(x) and g(x). Multiply (use FOIL). Combine like terms. Thus, (f Â· g)(x) = x4 + x2 - 30 (f Â· g)(x) = f(x) Â· g(x) = (x2 + 6) Â· (x2 - 5) = x4 - 5x2 + 6x2 - 30 = x4 + x2 - 30 Step 2 Use x = 3 to find (f Â· g)(3).Substitute 3 for x. Simplify. = (3)4 + (3)2 - 30 = 60

So, (f Â· g)(3) = 60

Example 2

Given f(x) = 12x3 - 18x and g(x) = 3x, find when x = -8. That is, find

Solution

 Step 1 Find Substitute for f(x) and g(x). Simplify. = 4x2 - 6 Step 2 Use x = -8 to find Substitute -8 for x. Simplify. = 4(-8)2 - 6= 250

Note:

One way to simplify is to factor and then cancel common factors:

A second way to simplify   is to write it as two fractions and then simplify each.