Decompose the function f(g(x))=(6x)^(8) into f(x) and g(x). g(x)= f(x)=

Identify Inner Function: To decompose the function f(g(x))=(6x)^(8) into f(x) and g(x), we need to identify a function g(x) that when input into another function f(x) will result in the given expression (6x)^(8).Choose g(x) as 6x: Let's choose g(x) to be the inner function that represents the part inside the parentheses before the exponentiation. A natural choice for g(x) would be 6x, since it is the base of the exponent in the given expression.Determine f(x) as x^8: Now we need to determine f(x) such that when g(x) is input into f(x), the result is (6x)^(8). Since g(x) is 6x, we want f(x) to be a function that raises its input to the 8th power. Therefore, f(x) should be x^(8).Verify Decomposition: To verify our decomposition, we can substitute g(x) into f(x) and check if we get the original function f(g(x))=(6x)^(8). Substituting g(x) into f(x), we get f(g(x)) = f(6x) = (6x)^(8), which matches the original function.

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Algebra 2

Simplify variable expressions using properties

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Q. Decompose the function

f(g(x))=(6 x)^{8}

into

f(x)

and

g(x)

\newline

g(x)=

\newline

f(x)=

Identify Inner Function: To decompose the function $f(g(x))=(6x)^{8}$ into $f(x)$ and $g(x)$ , we need to identify a function $g(x)$ that when input into another function $f(x)$ will result in the given expression $(6x)^{8}$ .
Choose $g(x)$ as $6x$ : Let's choose $g(x)$ to be the inner function that represents the part inside the parentheses before the exponentiation. A natural choice for $g(x)$ would be $6x$ , since it is the base of the exponent in the given expression.
Determine $f(x)$ as $x^8$ : Now we need to determine $f(x)$ such that when $g(x)$ is input into $f(x)$ , the result is $(6x)^{8}$ . Since $g(x)$ is $6x$ , we want $f(x)$ to be a function that raises its input to the $8$ th power. Therefore, $f(x)$ should be $x^8$ $1$ .
Verify Decomposition: To verify our decomposition, we can substitute $g(x)$ into $f(x)$ and check if we get the original function $f(g(x))=(6x)^{8}$ . Substituting $g(x)$ into $f(x)$ , we get $f(g(x)) = f(6x) = (6x)^{8}$ , which matches the original function.