Adding Functions. Subtracting Functions. Multiplying Functions. November 02, Algebra 2 Ch 3.3 Perform Function Operations and Composit.

Transcription

1 3.3 Perform Funcon Operaons and Composion Power funcons Add, subtract, mulply and divide funcons Composites of funcons Undefined Funcons In the past we have used functions such as f(x) and g(x), individually, but now we are going to use two functions at the same time. With functions, we are going to : add subtract multiply divide and do other things, such as find composites and inverses For all of the operations we are going to do today, will use the following two functions: Adding Functions Subtracting Functions Multiplying Functions 1

2 Multiplying Functions What does this mean??? What value can x not be equal to? STOP We say: h of 2 equals f of g of 2. We are still using these two functions: inner function Evaluate the inner function first, which is g(x), then take your answer and use that to evaluate the outer function, which is f(x). This is called a composite function. So first evaluate: We want to find this answer : But first we do this intermediate step : Now we can evaluate the function f : Now take this value and use it as the input for f(x) 2

3 Remember: SO: What we saw in the last example was how the domains and ranges of composite functions interact. The domain of the function g is 2. The range of the function g is 4. The domain of a function is its inputs, which are the x values. The range of a function is its outputs, which are the y values ( also f(x) ) The domain of the function f is 4, and its range is 65. When we create composites, the range of the inner function, becomes the domain of the outer function. Could there have been an easier way to find the answer of a composite function? Yes, we will find the composite????? equation of the two functions. 3

4 Outer Function Inner Function There was more work at the start of the problem, but now that we have found the composite, we can easily evaluate any value, rather than doing all of the work in the first method that we used. Now we will find Outer Function Inner Function Do you think that it will be the same as? 4

5 When we create a composite that contains a variable in the denominator, we must consider the domain, which are the input values of x. NOT EQUAL If x = 12, the value 12 is in the acceptable domain of x, so we can evaluate this function. Suppose you were going to buy a car, the dealer offers you a $2000 rebate and a 12% discount. If the sticker price of the car is $26,000, which offer would you like to apply first. Rebate Discount Discount first, then rebate. Discount first, then rebate. Rebate first, then discount. 5

6 Rebate first, then discount. Bonus Question At what price does it not matter if either the discount or rebate is taken first? To find the answer, set the two composites equal to each other. 3.3 Perform Funcon Operaons and Composion Power funcons Add, subtract, mulply and divide funcons Composites of funcons Undefined Funcons There is no answer to this question! 6