Finding Functions That Form a Given Composite (3.18.4) Flashcards
• The benefit of composing functions with each other is that you can follow one input through several processes to reach a final output.
• The benefit of composing functions with each other is that you can follow one input through several processes to reach a final output.
• Composition notation: f ◦ g indicates that f (x) will be evaluated with the output from g (x).
• Composition notation: f ◦ g indicates that f (x) will be evaluated with the output from g (x).
• Note carefully which function is going to be used first. Make sure that function’s output is used in the second function.
• Note carefully which function is going to be used first. Make sure that function’s output is used in the second function.
In this example, you are given the composition f ◦g and asked to name the two functions that could have been used to create this composition. You know that f ◦g (x) = f [g (x)]. In this case the only thing that g (x) could be is the expression (6x –2). So, set g (x) = 6x –2. That leaves f (x) = x^2. And that agrees with what the screen shows.
In this case, you are given that the composition f ◦ g = 2(4x –1)3 – (4x–1) + 3. It would appear that the equivalent of an x-term here is (4x –1). So, g (x) must equal (4x–1). If so, replacing every (4x –1) with x, we get f (x) equals 2x^3 – x + 3.
In this example, you are given the composition f ◦g and asked to name the two functions that could have been used to create this composition. You know that f ◦g (x) = f [g (x)]. In this case the only thing that g (x) could be is the expression (6x –2). So, set g (x) = 6x –2. That leaves f (x) = x^2. And that agrees with what the screen shows.
In this case, you are given that the composition f ◦ g = 2(4x –1)3 – (4x–1) + 3. It would appear that the equivalent of an x-term here is (4x –1). So, g (x) must equal (4x–1). If so, replacing every (4x –1) with x, we get f (x) equals 2x^3 – x + 3.
