Suppose $H(x)=(5-7 x)^{5}$.
Find two functions $f$ and $g$ such that $(f \circ g)(x)=H(x)$.
Neither function can be the identity function.
(There may be more than one correct answer.)
\[
\begin{array}{l}
f(x)= \\
g(x)=
\end{array}
\]

Answer

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Answer

Final Answer: \[\boxed{\begin{array}{l} f(x)=x^{5} \\ g(x)=5-7x \end{array}}\]

Steps

Step 1 ：We need to find two functions $f$ and $g$ such that the composition of $f$ and $g$ gives us the function $H(x)$. The function $H(x)$ can be broken down into two parts: the inner function $5-7x$ and the outer function $x^5$. We can use these two parts to define our functions $f$ and $g$.

Step 2 ：Final Answer: \[\boxed{\begin{array}{l} f(x)=x^{5} \\ g(x)=5-7x \end{array}}\]

Suppose $H(x)=(5-7 x)^{5}$.Find two functions $f$ and $g$ such that $(f \circ g)(x)=H(x)$.Neither function can be the identity function.(There may be more than one correct answer.)\[\begin{array}{l}f(x)= \\g(x)=\end{array}\]

Answer

Popular Problems

Suppose $H(x)=(5-7 x)^{5}$.
Find two functions $f$ and $g$ such that $(f \circ g)(x)=H(x)$.
Neither function can be the identity function.
(There may be more than one correct answer.)
\[
\begin{array}{l}
f(x)= \\
g(x)=
\end{array}
\]