Let $g(x)=x+6$. Find $f(x)$ so that $h(x)=(f \circ g)(x)$.
\[
h(x)=\sqrt{x+6}+5
\]
\[
f(x)=
\]

Answer

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Answer

The final answer is $f(x)=\sqrt{x}+5$

Steps

Step 1 ：Given that $h(x)=(f \circ g)(x)=\sqrt{x+6}+5$, we want to find $f(x)$.

Step 2 ：We know that $g(x)=x+6$, so we can substitute $g(x)$ into $h(x)$ to get $h(g(x))=\sqrt{g(x)+6}+5$

Step 3 ：Since $h(x)=(f \circ g)(x)$, we can equate $h(g(x))$ and $h(x)$ to find $f(x)$

Step 4 ：So, $f(x)=\sqrt{x+6}+5$

Step 5 ：Therefore, $f(x)=\sqrt{x}+5$

Step 6 ：Checking our result, we substitute $f(x)$ into $h(x)$ to get $h(x)=\sqrt{g(x)+6}+5=\sqrt{x+6}+5$, which is the original equation.

Step 7 ：So, our result is correct.

Step 8 ：The final answer is $f(x)=\sqrt{x}+5$