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Determine two simple functions who composition is $f g(x)$ ).$f(g(x))=\left(2 x^{8}-11 x^{5}-2 x+19\right)^{54}$

$$\begin{array}{l}f(x)=x^{54} \\g(x)=2 x^{8}-11 x^{5}-2 x+19\end{array}$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Missouri State University

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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02:02

Determine two simple funct…

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01:39

02:01

Find two functions $f$ and…

02:07

00:34

Express the function $F$ a…

01:59

02:26

Let g(x) = x 2. Find a fun…

02:04

Let $g(x)=x^{2}+3 .$ Find …

01:16

QUESTIONGiven two func…

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01:46

for this problem. We have been given a composite function f of G of X, and our goal is to break it apart into two pieces half of X and g of X. Now there are multiple ways that we could break this apart, but we're gonna look for two simple functions that we could have put together to create our composite function. So let's think about how composite functions work. I haven't outermost function that f function. So it's a function which I am plugging something else into to evaluate it so that something in the middle is the G of X. And actually, I'm going to even see if I can use that word, something to help us figure out what's going on here because I'm doing this outer function. F I'm taking f of something. Well, let's take a look at this right hand side. I'm raising something to the 54th power. It's a big, huge thing as I parentheses, but I'm raising something to the 54th Power. So that's something is my G of X function. That's what I'm raising to the 54th Power so that 54th power is the outside piece of my function. That's my F function. If you think about being a composite function, F of G of X means I'm calling my f function. But in place of X, I'm putting my G of X. That does give us the composite function that we saw up here. So this is one way to decompose it into an F function and a GI function.

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