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Determine two simple functions who composition is $f g(x)$ ).$f(g(x))=\left(3 x^{2}-2 x+23\right)^{18}$

$$f(x)=x^{18}, g(x)=3 x^{2}-2 x+23$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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for this problem. We have been given a composite function f of G of X, and our goal is to break this apart into two simple functions f of X and G of X. Now there are many different ways we can break this apart. But what's a nice you know, nice, simple basic functions and F energy that I could have put together to get this composite function Well, a good way to breaks apart is to remember what a composite function is. It is f being evaluated or be being considered at ah function. So the function is going into my F function. So what we're going to do here, this is often a good way to get started with ease. I don't know what that innermost function is. I'm just gonna say it's something. I'm going to get something out from G of X. So this is f of something. So let's see if I can use the word something in place of a piece of this composite function. And you know that if I could do that, whatever I say something for will be that g of X. So if I look at this, this is really something to the 18th power. So that innermost piece that's something is three X squared, minus two X plus 23. And I'm taking that something to the 18th power. So the outermost function is F, and the outermost piece of this function is raising something to the 18th power. So I could break this up into two functions F of X being X to the 18th power and G of X equaling three X squared minus two X plus 23. That piece, which I am raising to the 18th power it got. Eventually it was put in here for the composition.

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