How to find the product of functions
When you have multiple functions, you can use some simple rules to find their sum, difference, product, or quotient.
When you have multiple functions, you can use some simple rules to find their sum, difference, product, or quotient. In this video we're going to focus on how to find the product of two functions.
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0:12 // What is the "product of functions"?
0:23 // How to do you write the product of two functions?
1:01 // Multiplying functions that are numbers (constants)
1:31 // Multiplying functions that have variables
2:35 // Finding fg(2): the value of the product function at x=2
As you might guess, finding the product of functions is as simple multiplying the functions together. When you multiply two functions together, you'll get a third function as the result, and that third function will be the product of the two original functions.
For example, if you multiply f(x) and g(x), their product will be h(x)=fg(x), or h(x)=f(x)g(x). You can also evaluate the product at a particular point. So if you want to know the value of the product at x=2, you can plug x=2 into the product function h(x) to find h(2)=fg(2)=f(2)g(2).
Alternately, instead of first finding the product function, and then evaluating at x=2, you could first evaluate both f(x) and g(x) at x=2, and then multiply those results together to get the product h(2).