Express the function $$ h(x)=\frac{1}{x+8} $$ in the form $$ f \circ g $$. If $$ g(x)=(x+8) $$, find the function $$ f(x) $$ Your answer is $$ f(x)=\square $$

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Given the function $$ h(x) = \frac{1}{x+8} $$ and $$ g(x) = x + 8 $$, we want to express $$ h(x) $$ as a composition $$ h(x) = f(g(x)) $$.

Let's break it down:

1. **Start with $$ g(x) $$:**
   $$
   g(x) = x + 8
   $$

2. **Express $$ h(x) $$ using $$ f $$ and $$ g $$:**
   $$
   h(x) = f(g(x)) = f(x + 8)
   $$
   
   Given that:
   $$
   h(x) = \frac{1}{x + 8}
   $$
   
   We can equate the two expressions:
   $$
   f(x + 8) = \frac{1}{x + 8}
   $$
   
3. **Determine $$ f(x) $$:**
   
   To find $$ f(x) $$, let’s replace $$ x + 8 $$ with a new variable, say $$ u $$:
   $$
   f(u) = \frac{1}{u}
   $$
   
   Therefore, the function $$ f(x) $$ is:
   $$
   f(x) = \frac{1}{x}
   $$

**Answer:**
$$ f(x)=\dfrac{1}{\,x\,} $$
$$ f(x) = \frac{1}{x} $$

Express the function \( h(x)=\frac{1}{x+8} \) in the form \( f \circ g \). If \( g(x)=(x+8) \), find the function \( f(x) \) Your answer is \( f(x)=\square \)

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