Decompose the function f(g(x))=((1)/(x))^(6) into f(x) and g(x). g(x)= f(x)=

Identify Composite Function: To decompose the function f(g(x)) = (1/x)^6, we need to find two functions f(x) and g(x) such that when g(x) is plugged into f(x), we get the original composite function.Choose g(x): Let's choose g(x) to be a function that will simplify to give us an expression that looks like (1/x)^6 when plugged into another function f(x). A natural choice for g(x) is to take the reciprocal of x, so let's set g(x) = 1/x.Find f(x): Now we need to find a function f(x) such that when we plug g(x) into it, we get (1/x)^6. Since g(x) = 1/x, we want f(g(x)) = f(1/x) to equal (1/x)^6. Therefore, f(x) must take an input and raise it to the sixth power. So we can set f(x) = x^6.Verify Decomposition: To verify our decomposition, we can substitute g(x) into f(x) and check if we get the original function. Substituting g(x) into f(x), we get f(g(x)) = f(1/x) = (1/x)^6, which is indeed the original function.Final Functions: Therefore, the functions f(x) and g(x) that decompose f(g(x)) = (1/x)^6 are f(x) = x^6 and g(x) = 1/x.

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Decompose the function
f(g(x))=((1)/(x))^(6) into
f(x) and
g(x).

g(x)=

f(x)=

Decompose the function $f(g(x))=\left(\frac{1}{x}\right)^{6}$ into $f(x)$ and $g(x)$ . $\newline$ $g(x)=$ $\newline$ $f(x)=$

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Algebra 2

Find the vertex of the transformed function

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Q. Decompose the function

f(g(x))=\left(\frac{1}{x}\right)^{6}

into

f(x)

and

g(x)

\newline

g(x)=

\newline

f(x)=

Identify Composite Function: To decompose the function $f(g(x)) = (\frac{1}{x})^6$ , we need to find two functions $f(x)$ and $g(x)$ such that when $g(x)$ is plugged into $f(x)$ , we get the original composite function.
Choose $g(x)$ : Let's choose $g(x)$ to be a function that will simplify to give us an expression that looks like $(1/x)^6$ when plugged into another function $f(x)$ . A natural choice for $g(x)$ is to take the reciprocal of $x$ , so let's set $g(x) = 1/x$ .
Find $f(x)$ : Now we need to find a function $f(x)$ such that when we plug $g(x)$ into it, we get $(1/x)^6$ . Since $g(x) = 1/x$ , we want $f(g(x)) = f(1/x)$ to equal $(1/x)^6$ . Therefore, $f(x)$ must take an input and raise it to the sixth power. So we can set $f(x) = x^6$ .
Verify Decomposition: To verify our decomposition, we can substitute $g(x)$ into $f(x)$ and check if we get the original function. Substituting $g(x)$ into $f(x)$ , we get $f(g(x)) = f(\frac{1}{x}) = (\frac{1}{x})^6$ , which is indeed the original function.
Final Functions: Therefore, the functions $f(x)$ and $g(x)$ that decompose $f(g(x)) = (\frac{1}{x})^6$ are $f(x) = x^6$ and $g(x) = \frac{1}{x}$ .